Ooh. That took me ages... I started over 3 times. Those are not my 10 favourite songs I guess because if I would start over one more time the list would look different again. But they come close and stood the test of time for me. I think it looks a little different compared to the other lists. But hey... I'm strange... you don't have to understand me. I don't understand you either. I mean.... how can you pick GNR' Knockin' on Heaven's door when you can pick the original by Bob Dylan...

Oh, and I didn't use any Bon Jovi songs on purpose.
1. Sting - Shape of my heart
Yep. Sting. One of the best songwriters ever I think. And this song is his masterpiece in my opinion. I also like "It's probably me" a lot but only the version with Clapton.
2. Billy Joel - New York State of Mind
Don't like many Joel songs but this one is just awesome.
3. Elton John - Tiny Dancer
Don't like many Elton John songs either but this one is just.... well... awesome...
4. Counting Crows - Mr. Jones (Storyteller version)
Counting Crows rule. Right after Bon Jovi. It was hard to pick one song but I totally love this version of Mr. Jones.
5. Live - Dolphin's Cry
Saw them live in Berkley once (with Counting Crows). Didn't know them before and that's their best song.
6. Rage against the Machine - Killing in the name
Yep... Sometimes I'm in the mood.... I think they were cool as opposed to the Limp Bizkit & Co crap you get these days.
7. Bruce Springsteen - The River (Live Version from "1975 - 1985")
Could have picked Thunderroad, too but I think I like this version just a little better.
8. Melissa Etheridge - Like the way I do
I totally love hear unplugged stuff and saw her live on her "Live...and alone"-Tour. She rocked.
9. Tom Waits - Christmas Card from a Hooker in Minneapolis
He's the man. Don't like all of his stuff cause a lot of it is just weird and I think I'm not weird enough (yet) to get it. Just listening to this song right now.
10. Pearl Jam - Jeremy
Just great. Now I'm listening to that song.
(This one goes to eleven - Spinal Tap)
11. Tony Benet - I left my Heart in San Francisco.
haha.

Just based on personal reasons.
Appendix
I have to mention two guys I've left out because I couldn't decide what song I like best. The first one of course is Elvis. When I was 5 he made me play air guitar. The other one is... yes it's a little embarrassing now but i'm gonna tell you anyway... Joshua Kadison. I just love his storytelling.
Most of the songs I picked are for my "Starring-at-the-ceiling" mood (especially Kadison). That's just how I feel right now. So, if I was in a different mood I'd probably had other stuff picked.