Like Bones, Brain's Base was formed in the mid-nineties, but didn't get to producing any anime until the mid-2000s. Their first production was Kamichu, in 2005. It's hard to pin down their style since they have a pretty varied number of works. But there's still this air to it their stuff that's really them. It's kind of like trying to make a serious attempt at defining Canadians (a discussion that is regularly had among us).
「今日も晴天」 by ゑの
So yeah, Kamichu!. It's a fantastic slice of life show set in the 80s, where a girl somehow ends up becoming a local deity. It's kind of a look at what Shintoism could conceivably look like in the real world. It's also great because even though Yurie is a deity, she still has to deal with the problems that a middle school kid has (read: her crush).
「バッカーノ！」 by ナムナム
I heard you like Baccano. Gangsters carrying out a train heist in America during the Roaring Twenties combined with an elaborate multithreaded plot and a huge, unique, and eccentric cast of characters? Hells yes.
「紅-Kureni-」 by ぎん太郎
Kure-nai is an interesting adaptation. It's about a guy working as a dispute mediator who's taken on a job to hide a little girl from her extremely powerful family. It's a nice mixture of slice of life moments as the girl learns about the outside world and action as the guy punches dudes on the job. What's more interesting than its anime-original storyline is the very noticeable departure in art direction from the light novel. Also contains the best musical in anime to date.
「友とひまわりと先生と。」 by もは
Natsume Yuujinchou is a lot like Kamichu in that it's Shintoism in the real world. The difference is that while Kamichu is about the novelty of the different spirits and deities where such things are commonly accepted, Natsume Yuujinchou is about the social isolation that being the only one who can see these things brings. It's a beautiful series about acceptance, among both humans and youkai.
「デュラララ！！」 by CHRIS
Durarara!! is Baccano: Tokyo Edition for a variety of reasons, most of them having to do with the fact that Narita Ryohgo is behind both novels. In fact, much of the description can be reused: it's about gangsters carrying a, uh, gang war in Tokyo set during probably sometime now combined with an elaborate multithreaded plot and a huge, unique, and eccentric cast of characters. This one's a lot more popular than its older brother, likely because it's more culturally accessible to its target audience.
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Certainly, Brain's Base is not flawless. After all, they were responsible for Akikan, which, depending on how forgiving you are, is thought to be intentionally awful. Still, they have an excellent track record and did surprisingly good work when they picked up Spice and Wolf from Imagin. In the fall, they'll be working on Kuragehime, a weird show for the noitaminA timeslot. And further into the future? If they like money, more sequels to the above shows (except Kamichu, since that's finished) are incredibly likely (well, except maybe Baccano, because who knows).
