From what I've experienced it's clearly Shōnen. Besides Detective Conan thats pretty much the only type of anime one got to see on TV (in Germany, at least).
The most prevalent were (no surprises here) Yu-Gi-Oh, Pokemon, One Piece, Naruto, Dragonball Z, Inuyasha..
Shounen. It's so mainstream and a lot of anime have this type of genre in it. That and maybe comedy or ecchi or yaoi/yuri even. But I think shounen wins for most mainstream.
Shounen apparently. Its the only anime I ever watch...mainly because its the only ones that are ever aired here .____. People say I should watch other types of anime but I mean....shounen is pretty damn good. I like action. People who aren't really into anime, but watch a few seem to watch Shounen, and its the only genre I really hear. Only really dedicated anime fans seem to mention other types of genre and I most likely never heard of these shows.
Mainstream...basically, an anime that everyone's into? No, better definition; an anime that everyone knows. The casuals who say they're anime fans just because they watch a few things from this genre...the hardcore haters who fly into a rage the moment a specific series from this genre is even mentioned...Does such a thing exist?
Of course it does. Step aside, mecha; in this day in age, the Big Three are all shonen. The famous anime before the Big Three were also shonen. If you love anime, you've heard of them. If you don't care about anime, you've STILL heard of them. Naruto, Bleach, One Piece....series that just happened to be in the right place in the right time to become big hits.
Well, this is technically only true in the 'western' fandom, anyways.
Shounen. There's no denying it, really. XP However, just because it's mainstream, that doesn't make it bad. A lot of people seem to think it does and it annoys me... I've encountered countless fans on the internet who basically hate anything popular just because it's popular (e.g. Naruto/Naruto Shippuden, Bleach, One Piece, Fairy Tail, Death Note, though to be fair, I've never actually come across a Fullmetal Alchemist hater).
Shounen. If you say the word anime to anyone, what do you think they would say? Things like Naruto, Dragonball Z, and other things of that nature. It's impossible to go far in an anime fandom without hearing of some shounen anime or manga, and in all honesty, even people who dislike shounen have at least seen one. You hear more people talking about Inuyasha and Naruto than Ojamajo Doremi and Toradora, right?