I put entire albums on there if it's one of my favorite artists - for example, I have every single one of Bruce Springsteen's albums on there in their entirety. Same with The Tragically Hip, Pearl Jam, Dan Fogelberg, Alanis Morissette, Journey, Matchbox 20, The Police/Sting, Fleetwood Mac, and a few others.
I also have some 60's & 70's musicians where I don't necessarily have all their albums, but I put on the entirety of what I do have - Janis Joplin, Jimi Hendrix, The Doors, and Led Zeppelin, for example...or mixed 'temporary' groups like Blind Faith.
I also have a ton of classical music on my iPod, and of course I put entire albums on there in those cases.
But in the case of most other artists, I have only the songs I like. Or in a very few cases, I've downloaded a single song by an artist because of particular memories I have attached to that song. There are about 10 - 12 songs I have that no matter how much time goes by, these particular memories always pop into my head whenever I hear the song. Might not own the entire album...but I have these songs.