I think if you asked most seasoned magic players what the commonly regarded best colour in MtG was they would basically all say blue. I am obviously writing this from a cuber perspective, there are plenty of blocks and standard formats where blue has been weak. With this being from the perspective of cube it will also largely apply to legacy, vintage, EDH, the theoretical "best of all time" and also fairly well to modern. You could simply argue that blue has the best and most powerful individual cards which leads to it being the best colour. This is true but does not satisfactorily explain the whole of the why.
There are broadly speaking two kinds of cube, those that are powered and those that are not. I would assert that blue remains the most powerful colour in both but it is significantly closer in the unpowered cubes. Once you strip away the colourless cards from the power and older cards that are similarly above the curve you are basically only left with blue cards and Fastbond. I do not even consider Timetwister to be above the curve however Time Walk, Ancestral Recall and Mana Drain are all disgustingly over powered to the point I have banned them in my cube so as to have fairer more fun games. If I can satisfy why blue is the most powerful in an unpowered cube it should be fairly easy to accept that it is also the case in a powered one.
I shall start off by arguing some reasons why blue is weak as a colour and then try and explain what it is about blue cards that sufficiently offset these limitations such that blue can be considered the most powerful colour. If you are only allowed to build mono coloured decks then blue quickly becomes one of the weakest colours. It has weaker creatures in terms of their potency in combat and presence on the board. It is also the shallowest in terms of creature quality, it has some very powerful ones but remove them and you are not left with much at all. Blue leans very hard on artifacts when being played as mono to support it in the areas in which it is weaker. Blue can compete as mono but it has to be built with what your opponents are doing heavily in mind, stretch it too far and it has no hope but you can tune it to deal with several different decks fairly well. Blue cannot destroy things, this is the main weakness of the colour along with flimsy minions. Typically it is for destroying things that you employ artifacts in mono blue decks. Not being able to directly destroy things means that you are vulnerable to all manner of things people can put into play. A Grim Lavamancer can be death to anything you can play, an early Ankh of Mishra can be too much damage. Certainly blue can counter things or bounce them or both, it can even just steal them. This is typically fine against the larger permanents but it is far too inefficient against cheaper cards.
Every colour has strengths and weaknesses. This discussion about blue in mono covers the weaknesses of blue and also suggests that those weaknesses are more severe in blue than they are in other colours. This would stand to reason as it would somewhat balance the extreme positives of the colour. The thing is, magic is a game where you can mix and match your colours and design your decks. Some of the best cards are those with drawbacks that you can, through deck design, mitigate such that you have a greatly over powered card. Broadly speaking this is why blue is so good, you can exploit it strengths while mitigating its weaknesses using clever design and the qualities of other colours.
So, what are these exploitable strengths that blue has and what is it about them that makes them stand out above all the other colours. I would group blues strengths into three categories of card types; counterspells, card draw and card quality. Counterspells are almost entirely unique to blue, those few that there are outside the colour are typically far too niche for cube play or are just complete shite. Card quality is becoming more available to other colours but blue still has the most, the best and the cheapest of the card quality spells. It has all the most generic library and hand manipulation as well as the best of the more universal scry cards. Card advantage is also becoming more available to other colours in many different forms, typically this is through incremental advantages on the likes of planeswalkers or two for one style creatures. Blue has card advantage of this kind and some pretty good effects at that but it also has lots of card advantage that offers that advantage as cards in hand rather than your dork back or two effects in one spell etc. Cards in hand is obviously the most rounded and generic form of card advantage, it allows you to do whatever you want with those cards and your deck design. Outside of blue it is both rare and difficult to get a grip full of juicy cards from your library. Black has some tools like Necropotence but they are painful and need to be very carefully built around. Green has some stuff but they all require you to have loads of dorks in play or cast loads of dorks to trigger. Red has, er, Wheel of Fortune. If you just want a card that costs some mana and does little more than leaving you with a bigger hand than before you cast it you really have to look to blue.
All three of blues strengths are pretty exclusive to blue. Some other colours have a pretty exclusive thing, direct damage in red, permanent ramp in green (although artifacts can adequately fulfil this role), discard effects in black, but it is one thing not three, and excluding red's direct damage not in quite the same league as the blue stuff. Blue might have weaker creatures but it still has creatures, no other colour has counterspells. Removal and creatures being the weakness of blue make it very easy to offset. All the other colours have stronger monsters and are much more comparable in overall strength than the blue ones are so you can go blue X and happily have monsters that will go toe to toe with other decks. Likewise with removal, blue can deal with stuff in a roundabout way, it is like having weaker creatures. All other colours have removal for some permanent types so your given blue X pairing will not only sort you out for dorks but it will cover you pretty well for removal too. Having unique strengths is great as it means everything can gain access to new tools by pairing with you and likewise, having unique weaknesses is also good as it means help is at hand wherever you look for it.
I recently did an article on card quality that goes into some detail about why it is so good and which cards are the best for cube use. Unsurprisingly the list was predominantly blue and almost all the outlying cards that did not make the top X were also blue. Put simply rather than in 10,000 words or so... magic is a random game. Card quality reduces the randomness and makes you more consistent. Lots of games are lost through floods and screws and card quality is some insurance against those losses you cannot do anything about. It is not just insurance but also gives you the ability to outplay people in the more even games. Card quality spells give you a lot more options and much more immediacy on those options than most other types of cards, especially if we are talking choices per mana spent. Choices let you play the game and let you use more skill as well as luck and card power to win games.
Before we go on to look at countermagic I want to consider the scaling effect of card draw and card quality. At the start of this article I commented that this was from the perspective of cube but it would also apply to a bunch of other formats, apply reasonably to modern, but not always to the standard and block formats. While some blocks just fail to support some colours well this is not the only reason behind the trend of having a larger pool of cards and blue becoming more powerful and vice versa, blue being weaker in smaller pools. Card quality and card draw generically scale well with power. The more powerful cards you have the more value there is on drawing more of them or having the right ones at the right time. Good creatures or say, burn spells don't have quite the same inbuilt scaling with the power of other cards. Not only are card draw and quality effects very good in their own right or in a vacuum so to speak, they are able to become more and more powerful based on the power of what you put them with. Thus, the broadest and biggest formats like cube are where the potency of blue is most noticeable.
A small side note on this general area which applies far more to powered cubes but still bears some relevance to unpowered cubes; Blue has the most synergy with artifacts as part of its colour pie flavour. Blue just has more cards that interact and scale well with artifacts than any other colour. Red is close but the other three barely do anything useful with them! Much like the scaling of card quality and card advantage with powerful cards, blue in general scales well with the power and number of the available artifacts in a given format.
There is even the simple argument that good cards make other cards better. I have already used the hateful phrase "in a vacuum" in this essay but it is a fairly useless concept in magic. There is no vacuum, cards necessarily interact with each other. A good card in blue brings up the quality of the other blue cards as they are easier to play with this one good card. The more good cards you add into this generic pool of good cards the better the total resulting power is. Blue has a great depth of very good cards, all of which make each other and the more average cards that much better overall. It is almost getting a bit chicken and egg saying that blue has a lot of great cards because blue has a great cards but at least Wittgenstien would approve. It is more like capitalism, once you (or blue in this metaphor) are rich and powerful it is far easier to become more rich and powerful.
You might argue that black has good protection against spells through the use of discard and this is true to some extent but really that is like comparing bounce to hard removal. A Duress will perform much the same role as a counterspell should you a; cast it before they can cast their offending spell. b; cast it after they draw the offending spell which is of course not always possible. You also need to fire off your Duress before they empty their hand of spells else it will achieve nothing. Sure, Duress is half the price of Counterspell and doesn't require you to have the mana available at quite such a specific time but it is still substantially weaker and less safe. Discard is typically used as stall, disruption that will buy you a good amount of time and be awkward. It is not used as a way to lock down anything scary your opponent might do, rather obviously because it would fail horribly in this task!
This is the crux of why countermagic is so strong. It is the only thing that provides protection against spells in any sort of reliable or ongoing way. On top of this exclusive spell protection countermagic typically provides a general form of removal/disruption. Dissipate does basically the same as Council's Judgement for any spell that makes permanents and it effects instants and sorceries too! Cancel does most of what Maelstrom Pulse does and more. Yes, you have to have the counterspell and the mana for it at the right time which is not the case for the removal spells but this is a small price to pay for such a powerful effect and that only makes up a part of what the card does for you.
Let us look at Tinker, another sick powerful blue card! The options available to other colours to be able to deal with Tinker are as follows, black has to hit it with a discard spell before cast and after drawn or deal with the thing it gets. Every other colour has to deal with the thing it gets. I guess white could respond with a Containment priest but this is the kind of specific sideboard nonsense that you don't want to have to resort to. Blue knows most colours will just have to try and deal with the thing they get with Tinker and typically plays a few things that each colour really struggles with. Red and green pretty much can't deal with a Sphinx of the Steel Wind so that is a nice easy win. Blue folds pretty hard to an Inkwell Leviathan. Black and white can be a little trickier to present an unkillable threat to but you can still make it awkward as hell for them. Black does not have an easy time with the cheap Wurmcoil Engine for example. The point is Tinker is a cheap spell that you can do really very little about efficiently or comfortably outside of blue or lucky black and Tinker is just one such example of a powerful spell that is hard to disrupt well.
Counterspells are typically associated with control but this is not because they are only good in control, quite the opposite. Countermagic is usually found in control because it is very difficult indeed to make a deck capable of dealing with all the things a cube can throw at you without countermagic. There are some very good aggressive strategies that employ countermagic to good effect too. Countermagic is great at protecting you, it is like good generic removal as well as good generic disruption. It will ease the burden on your pure removal cards and it will force your opponent to play with more caution and restraint.
I would agree that Actual Counterspell is somewhat above the curve and a big part of why so many magic players hate countermagic. Negate, Mana Leak and something like Dissolve are far fairer and more balanced examples of what countermagic should be. These fair counterspells represent the bottom end of what is good in cube, I don't even have a Dissolve in mine favouring Forbid in that slot. Fair counterspells still represent an exclusive thing in magic and still offer the best kind of safety against spells. Blue however has plenty of unfair ones which only serve to make the colour even more powerful. If the Forces of Will, Mana Drains, Arcane Denials, Cryptic Commands, Remands and Spell Pierces were never printed I am pretty sure the cube would still have a similar total number of counterspell style cards, it would just play more of the weaker ones in their place.
Countermagic is powerful in principle because it is an exclusive effect that is broad in application. It is the only real protection against instants and sorceries yet it does a good job of doing the role of your Vindicates and Hero's Downfall. It too scales well with and against powerful cards and also scales well with broadening and diversifying formats. With all this going for them those counterspells that fall above the curve gain a lot in power very quickly.
There we have it, the collection of reasons why blue is the best colour as far as I can discern them.