I like classics and modern games, in parenthesis are games that I've played and enjoyed from the following series:
Mario (3, World, New Super Mario Bros DS/Wii, Super Mario 64 DS)
Sonic the Hedgehog (1/2/3&K, CD on XBLA, Adventure, Heroes, Unleashed daytime and Generations - most of the mothership titles, really)
Tomb Raider (The first five and their expansion packs, I have AoD and it went downhill from there, in my opinion)
Halo (3, ODST & Reach)
Tales of.. (Symphonia, Abyss)
Super Smash Brothers (All of them)
To be honest, I'm not of fan of that many series because gameplay is essential to me and I'm really picky when it comes to that. When I do find a series in which I find the gameplay to be fun, I tend to stick to it. Take Sonic the Hedgehog for example, I've played just about all the mothership titles except Colours, to be honest.