I'm a HUGE grunge and alternative fan, but only of a select few, the biggest of which is Alice in Chains and Soundgarden. AIC influenced me the same way that old Metallica did, though in a deeper way. Metallica was something that made me start playing guitar, but AIC made me understand feeling over ability. For me, Chris Cornell during his Soundgarden years was the greatest frontman of all time. I know that's a bold statement, but that's how I feel about it. I dug only a few songs from Nirvana, but mostly I was sick of all the hype.
I also like REAL country, as Shpongled said.
The music that can bring me to tears, however, would be classical. The wif is a classically trained violinist, so there's no shortage of inspiration to draw from in this house. I prefer Grieg and the like instead of Vivaldi and Paganini. Vivaldi is so overplayed and actually overrated in my opinion. Genius, yes, but the conservatories here play just like Vivaldi: perfect in every way and with absolutely no feeling.
Since I grew up in the 80's, of course I love a lot of 80's bands, and I don't mean only metal bands. J. Geils Band, Springsteen, Yes, The Fixx, Tears for Fears, Rick Springfield, etc. Also a lot of 70's bands that I grew up with through my parents, such as Skynyrd, Allman Bros., ZZ Top, Peter Frampton, Creedence Clearwater Revival, Elton John, Pink Floyd, a little Zeppelin, etc. I hate the Eagles.