My **usual** preference is to listen to the entire album. Further, I've found I prefer to listen to an artist's entire (original, not "best of") album, as the collection of songs usually provides a context that makes the whole greater than the sum of parts.
That said, I on occasion like to listen to random songs - and random genre's which the Ipod is great at serving up in "shuffle play" mode.
As for how it came about - I guess in the beginning I only bought vinyl albums and played them on a fully manual table. When I bought my first multidisc cd player with shuffle mode, I found it was everything I wanted from FM - random music, no talk. But I also learned that after listening in shuffle mode for some time, the context for the songs was lacking.