Ready for a fairly in-depth answer? Here we go!
Pre-2002 my favourite genre would have been 'whatever Ocarina of Time is. I wouldn't have been able to come up with 'action-adventure with RPG elements,' (or however you want to classify OoT) because OoT was the only game in that genre that I'd played. My N64 was my only console. It was the first game I got with my N64, and remained my favourite for years. I quite literally must have beaten it close to 30 times. Looking back, I can't even tell you what it was about the game that struck me so hard, but, whatever it was, it got me hooked.
By 2002 it would have become 'whatever Ocarina of Time and Majora's Mask are: those were my two favourite games OF ALL TIME, (and they still rank pretty high on my list), and I would have wanted to play anything at all the reminded me of them.
By 2003, my favourite genre would have become RPG (not JRPG, because, at the time, I didn't know the distinction), because when I got my PlayStation 2, the first (and for a while only) game I got for it was Final Fantasy X. That was my introduction to the FF series, and for that reason, it is still my favourite Final Fantasy game. I kid you not when I say that for the 2 weeks I was home from school for Christmas holidays, I would wake up in the morning, ignore breakfast, play FFX until I got hungry (usually) around dinner, shower after I ate, and then jump right back into the game until I got tired (usually) around midnight. My parents were quite glad when school started up again. I think I worried them.
RPGs are still my favourite genre, and I play them every chance I get. It's been a while since I've played one that really struck me, though. Then again, I'm not wowed by many games these days. Maybe I'm outgrowing gaming as a hobby, I don't know. I certainly seem to play them less and less, despite the fact that I desperately try to keep up with all the new releases.
BONUS ANSWER: Least favourite genre: first-person shooters. Unlike the wonderfulness of Ocarina of Time or the time-sink of Final Fantasy X, I can't honestly pinpoint a game that made me dislike the genre. I think it's just because I don't find very much enjoyment in shooting things over and over again. I still play first-person shooters, but I don't own many of them, and really, most of the time I just play them because my friends do.