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Here's a challenge for you... lets list as many "Best of" albums as we can that aren't just "heres the singles that sold most and goyt us a lot of dosh" albums.... all albums posted must meet the following criteria...
1 The album must contain at least four tracks that were never released as singles
2 The album must contain at least one song that is incredibly popular at a live gig, that was never released as a single
3 The album must be a single artist/group compilation (so The Best of Atlantic Records," or "HMV Playlist" is out...

I'll start with Tori Amos's Tales of a Librarian... lets go....

do greatest hits count?

I'm guessing that Zombie - "Past, Present, and Future" qualifies.

The Essential Clash- The Clash

Only if at least four of the tracks on them weren't singles, and therefore weren't hits.....

guess the answer is no then

Isn't that the point of 'Best of's though? They are for the casual fan, live tracks and unreleased songs are more for rarities albums.

But surely best of should mean best, not most profitable.... unless you believe that best=most profitable, and that the Toyota Corolla is the best car in the world....

I don't personally, but that's how it tends to go.

Anyway to answer your question, I cannot think of one fitting your criteria, which essentially covers both of those points.

Best of, Singles, and Greatest Hits usually are all just singles.

Best of Smashing Pumpkins
Best of 311