I am a huge Metallica-fan, and I play a lot of their songs. To learn some more styles I would like some songs I could learn. I have decided for Joe Satriani's Always with me, Always with you, but I would like some more suggestions.

Sondre

What kind of styles are you looking for? Metal, Rock, Progressive, possibly some other?

Satch's Always with me is a great song to learn.
It will halp your legato, tapping, rhythm placement and all that stayiong melodic.
Plus, Satch being Kirk's guitar teacher, it's a good match!

I'm not sure if you're asking only about more Satch's tune
but here are few that I can think of atm (kind of easier ones):
-Memories, Hordes of Locusts, Rubina ( Not Of This Earth )
-Ice 9, Echo, Crushing Day ( Surfing With The Alien )
-Flying in a Blue Dream, I Believe, Big Bad Moon, The Forgotten Pt. II ( Flying in a Blue Dream )
-The Extremist, Cryin', Summer Song, Friends ( The Extremist )
-Time Machine, All Alone, Crazy (Time Machine)
-Cool #9, Down, Down, Down, Home, Morrocan Sunset ( Joe Satriani )
-House Full of Bullets, Time ( Crystal Planet )

Cheers.

Maybe check out Trivium, there often compared to Metallica . They have some easier songs to, and some harder ones.

Thanks all, alot of great songs.

Muris, I wasnt thinking of any spesific artists, I play alot Metallica, but want to learn other styles, and other guitar players style.Anything is good, as long as it is awesome!

kings of convenience !

Ahh ok.
Well, maybe it's not ok since there are trillion awesome bands and artists
that you can learn a lot from.
Some of my fav are Mark Knopfler (Dire Straits), David Gilmour (Pink Floyd),
Steve Lukather (Toto), Brain May (Queen) etc.
These might be kind a vintage players
but they are more than awesome.

Maybe you should just make a list of 5 bands and then go and learn their most famous song (choose one which you can play). To make it fun choose some bands like : Scorpions, Iron Maiden, Red Hot Chili Peppers , Beatles , Offspring
Those are 5 completely different songs then , it can be fun