Normally I at least wait until I have played with the card in question a few times before I spotlight it however this little artifact is especially interesting. It is not a broken card by any means but it is very powerful if used in the right places. Obviously I have a few ideas as to what those right places might look like which we will get to.
There are some cards that spring to mind that will help compare and contrast the Brain in a Jar and therefor give us a better idea of what to expect from it. The obvious first comparison is Aether Vial. Both are relatively cheap artifacts with a similar mechanic allowing you to incrementally play more expensive cards of a type both at instant speed and at growing discounts. Aether Vial gets around counter magic and is a much more potent accelerator. As soon as you flop in a two drop with Aether Vial you are mana up, you have to curve all the way to three with Brain in a Jar before you see your first saved mana. If you are purely interested in the mana saving abilities of Brain in a Jar then I suggest playing Talisman / Signets instead. Although very similar to the effects of ramp both Jar and Vial are best off at giving you those big powerful turns. Although you don't gain much the first few turns after making Vial or Jar you will be able to do twice as much on your mid and late turns which is hopefully enough to break the back of the game you are in and take a win.
Aether Vial is a much better early play than Jar, obviously they go in very different decks and so this comparison is not overly practical but it should at least yield insight into the cards. Vial wants a very high creature count while Jar wants a very high spell count, Naturally this means Vial goes in aggro decks while Jar will find itself more suited to control or combo. Aggro decks rely more on tempo and so a late Vial does little. Control and combo are much more about big turns and so a late Jar will still be decent. This is further made the case with the unique ability to lower the counters on the Jar and gain some scry for doing so. It is not a cost effective ability however if you are at that stage it already has and hopefully will again more than pay for itself. Jar will be able to provide ongoing utility while Vile rapidly becomes dead weight.
The next card I want to compare Brain in a Jar to is Birthing Pod. This comparison is much more specific to cube than constructed 60 card non-singleton formats where it shouldn't hold true in the same way at all. When building with Birthing Pod in the cube you need to be fairly careful about your curve, specifically in regards to creatures. With only 40 deck slots and a desire to have at least 3 decent targets at each point on your Pod's range you run out of slots in your list very quickly. If you don't give proper attention to your curve then you will find you have far too many turns where you Pod and now Jar will not do any thing for you. As both are cards that require an initial tempo investment before you can start to really abuse them you really cannot afford to have them sat idle that often.
Here are two examples of decks where the Jar shines:
Swords to Plowshares
Brain in a Bottle
Fact or Fiction
Wrath of God
So this is the control list I find most suited to Brain in a Bottle. It is incredibly spell heavy with a count of 21 which is likely more than you need for the Bottle to be strong. Spell heavy control lists have been on the decline since the introduction on planeswalkers and then powerful and abundant manlands. Slowly the available spell removal options for those threats have improved and so Brain in a Jar may be enough to allow a return to such style of control deck.
Not only does control hugely benefit from being able to have those big turns but it also gains a huge boost from having sorcery speed cards playable at instant. Bottle turns normal expensive slow Wrath effects into miracle Terminus level cards.
Another thing Jar encourages you to do is play card draw spells. You want to ensure you have a grip full of gas so as to have options on your Jar activations. Card draw spells are often too slow and/or expensive to be commonly played over card advantage generating permanents and so they have gone into a decline, certainly those without delve! Jar gives you the chance to play things like Fact or Fiction for 1 mana making it somewhat better than a Treasure Cruise! All told I don't think this list is insane or anything, I just think you can get it to work and beat the things it needs to. It will work OK without a Jar but it will become abusive if you get a good Jar draw and live long enough to charge it to up a bit. The list probably needs a recursion tool, the spell heavy decks tend to need specific spells multiple times in some matchups and you simply can't have redundancy in every area. These lists are more examples than optimized recommendations.
Brain in a Jar
Fact or Fiction
Order of Sucession / Pull from the Deep /
Unexpected Results/ Whelming Wave / Gifts Ungiven
Jace, the Mind Sculptor
17 Lands (including some manlands)
To my surprise I have never showcased this style of deck before. It is usually what you end up with when your storm deck goes wrong. Rather than go off and have one big turn it kind of goes off and never stops. It doesn't actually do much to win other than cast so many Time Walk effects that the game is over. There is no real combo, you just reach a critical mass of mana and have so much card draw than you can loop you deck long enough to get the job done. Brain in a Bottle could be OK in a storm deck as it might help a bit to setup the big turn and will provide a mana saving on that turn but it doesn't sounds worth it. In this kind of deck the Brain in a Bottle just keeps getting better, you shouldn't run out of spells and you will have more mana to adjust the counters and do some scrying.
There was a modern deck a while back that did well at a GP I think that used Aether Vial to play Eternal Witness and then cycle a loop of that and Cryptic Commands to lock down a game. This deck works fairly similarly to that using Time Warp effects as redundancy for Cryptic Command. This list, like the previous is not perfect. I couldn't even decide on the last few spells so threw in a load of options for the four slot which was lacking. As such I have overdone it and should add another 3 CMC card that Jar can play, if you are going the Gifts route it probably needs to be a Recollect (part of the reason Gifts is a much weaker card in 40 cards decks). These decks are hard to play and take a long time to get a win. They are also somewhat un-interactive and so all your friends will hate you for playing it.
So, there are some ways you can play the bottle. There are some significant overlaps between the two decks despite them having highly distinct play styles. You may also be able to get a burn deck to work with the Jar but you would need to play a lot more card draw than normal making the deck clunky when you didn't get the Jar. Cards that require that much polarization of a deck to utilize while having no real redundancy for its effect are often better not bothering with. Consistency is king, especially in linear decks like burn.
The Jar is one of the more powerful cards printed in recent years however it is incredibly balanced by how much work you need to put into your build to obtain that power. In constructed where you can play 4 of them I expect it to be a little more exciting. Realistically I don't even think you can get enough of our Brain in a Jar in a draft cube meaning it will sit in the B cube with cards like Isochron Scepter. Blue has the best spells and so most Brain decks will be heavy blue. It is one of those cards that despite being narrow and often winding up last pick it is still powerful enough to live in the cube and should be really fun when you do get enough cards to play with it.