Holy shit my hero was mentioned. Excellent suggestion by the way. Always with me always with you is one of my favorites. Here are some more suggestions:
Despite Kirk Hammetts' on/off musicality, to get my fingers going when I first started playing I built up the solos at the end of One and Fade to Black. They REALLY helped me out a lot as far as improving my dexterity.
Pantera - This Love: the riff at about 2'47" was something that helped me get my downpicking down (of course Master of Puppets did that, too. While we're talking about Metallica, at 3'16" in Seek and Destroy there is a badass riff to learn downpicking)
Pantera - Cemetary Gates: the famous pinch harmonic riff really got me started on learning those and helped me out a lot
Hmmm..... What else...... Vibrato: Joe Satriani - Mountain Song. Gotta love it.
Lamb of God - these guys kick ass. I can remember playing Laid to Rest all day to build up downpicking/alternate picking mixtures as well as dexterity
Okay here's a really random one. Van Halen's Hot for Teacher helped me with tapping. Don't diss.