My favourite SEGA games? Probably the Yakuza series and Jet Set Radio/Future. I enjoyed what I played of Valkyria Chronicles too but the difficulty curve meant that I never got to far into the first game. Outrun & After Burner are great titles as well.
And Samba de Amigo is worth a mention for the music alone.
I wrote an article on my upbringing on SEGA game's somewhere. My fave's are the obvious ones (sonic) and a game called Flashback. Aladdin was pretty awesome to
I'll say that my favorites series are Sonic, Outrun, Super Monkey Ball and NiGHTS.
Although not originated from SEGA, Puyo Puyo, if it counts that they own it now.
Yes, It's very difficult to choose favorites... My favs are NiGHTS, OutRun, JSR (of course) Crazy Taxi, Panzer Dragoon, (can't think of any more right now)
Sonic the Hedgehog, Nights, Panzer Dragoon (Saga + Orta), Jet Set Radio + Future, Ristar, Shenmue 1&2, Bayonetta, Space Harrier, After Burner, Fantasy Zone, and so many more to list