Anything that moves.
Hm? Doesn't make sense? Of course it doesn't; I didn't say shit.
Usually anything with a detectable degree of emotion. Something that speaks with or without lyrics. The Beatles (hah, even though I came in two or three--not really counting--generations late) are one of my favourite bands just for this reason. Blackbird, Good Day Sunshine and Michelle are great examples. Try listening to them without paying attention to the lyrics, there's still a lot of feeling and a very visible meaning.
Failing that, Indie Rock is probably the genre from which most of my other favourite bands stem, probably because it's similar to the old pop rock in a lot of ways. At least, the songs I listen to are.
I can also go for some alternative, punk rock, jazz and similar genres, and even some of that weird 70's-80's goth stuff (mostly Bauhaus) if I'm in the mood for a quiet laugh.
It's so weird it's funny.