My favorite Bomberman games are the N64 ones and Saturn Bomberman is my favorite 2D one. I haven't really followed the series for a number of years, and my newest game is Bomberman Jetters on the Gamecube which I have yet to finish. Though it wasn't too bad..
I can't say I'm too familiar with the Rayman series. Never really gave it a shot.
And I am quite an avid anime fan, or rather more like an otaku. lol.