R&B, Soul, Glam Rock, mainstream Pop. Mostly I like old Soul artists like Aretha and Whitney, though I only like a few of their songs. Mariah Carey on the other hand has a lot of songs I like, but I definitely would have liked them better if the former two sang them.
While I like a wide range of bands, most of them have some tie/resemblance to the Glam Rock genre (Guns N' Roses, Queen). I also like David Bowie who is kinda sorta influenced by Glam, rrrrrrrrrrrrrrright?
I've nothing against Katy Perry and Lady Gaga, but it's a rare occasion when one of their songs find their way into my iPod. Incidentally, all of the mainstream artists I like are British (Jessie J, Adele, Florence & The Machine).
tl;dr: R&B, Soul, Glam Rock, mainstream Pop.