It totally depends on the album for me. If I enjoy the whole album I'll happily listen through the whole thing, but I also listen to a lot of prog which has lots of concept albums where listening through the whole thing is kind of intended in another way since the whole record tends to tell a complete story.
But I usually just listen to playlists I make of music I enjoy, but those two ways of listening aren't like exclusive. It just depends on the album, and what I feel like doing at that time.
My favorite album is probably Operation Mindcrime, and I tend to listen to the whole record straight through, but I always skip one song because I think it's way weaker than the rest of the album.