I've watched countless anime in my time but for some reason I've always managed to skip the big names like Bleach, One Piece, FMA, etc, so now I'm going through catching up with some of those. My friend has just introduced me to Full Metal Alchemist by showing me the first two episodes and now I literally can't stop watching it (I'm even watching it whilst writing this post), it's just sooo good. Then next on my list is One Piece since I've heard great things about the main character and pirates are awesome!
As for manga, I've never really had access to much of it or known where to find it so I've not actually read any yet. D: