Pretty much anything by Miles Davis, John Coltrane or Charlie Parker. I’ve always loved instrumental Jazz.
I really love the theme from The Deer Hunter, and I can’t for the life of me remember the name of it. It’s just beautiful.
No (twice times two). 
Don Reno - Green Mountain Hop
“End Theme” by Zero7.
It’s gorgeous.
Mozart’s Serenade in G-the rondo-K525
“Little Martha” by the Allman Brothers. Perfection.
i like lots of New-Agey type stuff…
Pretty much anything by Tangerine Dream. Isao Tomita’s Snowflakes are Dancing, which features modern classical works performed on synthesizers and of course, Mike Oldfield’s Tubular Bells. And oddly, amongst all this new agey stuff, I love The Ventures!.
Apocalyptica. Especially “Nothing Else Matters.” I wish I’d known about them back in high school, when I played the cello (poorly).
“Sun Goddess” by Earth, Wind and Fire (there’s some “Ahhh” type vocals but no words, so I hope it counts).
I’d have to go with an Allmans song as well. Almost pointless to ask which one… maybe In Memory of Elizabeth Reed, maybe Mountain Jam, maybe Little Martha…
Porno Creep by KoRn, Hargalaten by In Flames, and another not-quite-an-instrumental-but-still-kinda-sorta-one that I can’t remember the name of. ^^;
D’oh! Three seconds after I clicked the button! >.< Anesthesia by Cliff Burton.
Birdland, by Weather Report
Jessica, by the Allman Bros.
Sing Sing Sing, Benny Goodman, live at Carnegie Hall
“Gabriel’s Oboe,” by Ennio Morricone from the soundtrack to The Mission. I have other faves, but this is at the top of the list for non-classical pieces. BTW, I also like Snowflakes are Dancing.
Cast Your Fate To The Windand Linus and Lucy - Vince Guaraldi Trio
“Uselink” by Depeche Mode. It molds beautifully into the next song, “Useless”.
Arrival of the Queen of Sheba by GF Handel
And, non classical: Serra Pelada by Philip Glass
Root Beer Rag by Billy Joel. It’s buried on Streetlife Serenade, so you have to be pretty hardcore to know it, but it kicks ass. It’s also damn near impossible to play.
Honorable mention to Theme From Dr. Pyser by Ben Folds Five, a B-side in the U.S. and bonus track on the Aussie version of Reinhold Messner.
Currently (because I’ve been listening to them a lot lately) I’d have to say that the Kronos String Quartet’s cover of ** Purple Haze** is my favorite.l The entire soundtrack from **Requim for a Dream **, which was also performed by Kronos, also deserves mention as a favorite instrumental.
Of course any “favorite” poll is pretty much useless for me since I’ll have a new favorite next week.