My favorite genres tend to come from the 60s and 70s. Especially soft rock, soul/R&B, progressive rock/psychedelic rock, and brass rock. I also love British Folk/Folk Rock. Classically I really like music from the eras of Baroque, Impressionist, Early Music (Medieval and Renaissance), and um...Classical (you know, Mozart, Haydn, early Beethoven).
A lot of my reasons for liking them comes down to instrumentation. I like a wide variety of instruments, especially woodwinds and brass. I like the hammond organ of the 60s, and the harpsichord. Now, that's not my only reason for liking them. I could go different directions with why I like Folk, progressive/psychedelic rock. Although Folk also sometimes includes fun early music instruments, like crumhorns!
My least favorite genres... Well, according to one coworker, I "don't like anything". You be the judge. =P
I really dislike Country. It's always either one of two things: Irritating as heck, or depressing. I listen to a lot of depressing music, but depressing Country zaps all of the enthusiasm out of me.
Metal, too. I can not stand anything with screaming, that automatically ruins the music for me. Yes, even Folk Metal. I've always found it to be incredibly cheesy. I don't know how, but they manage to suck everything out of Folk Metal that makes Folk so amazing.
80s Pop/Rock is also very low on my list. It's the decade when they really started going overboard with electronic components, IMO. And boy did the 80s go overboard. Even when the songs are less electronic, I usually don't like them. They just have a completely different feel than the two decades before.
Modern pop suffers from some of the same reasons as the 80s. Except unlike the 80s, modern pop isn't typically what I'd call cheesy, it's become so electronic that it's flat out hollow. It's very dry, devoid of anything likable.