FoldIt's productive for someone: http://fold.it/

Then there's the currency trade in most MMOs. That can be quite productive, from what I hear.

I personally avoid Minecraft because I feel some games are somewhat productive, and that Minecraft is not one of them.

I get the impression a very large part of Minecraft is mindless worker-ant operations. Compared to, say, Portal, I feel my time is better spent with the latter- even though neither produce a tangible product or any apparent immediate benefit. (Not to mention the fact that Portal has an ending, instead of going forever)

It depends on the game, but simulation games can be good for learning/honing the meta-skill of systems thinking, imo (in the sense of http://en.wikipedia.org/wiki/Systems_thinking).

Some hone skills that are broader than just that particular niche game.

e.g., chess and go hone the mind.

Minecraft could be used to hone some level of engineering thinking.

Sports hones the body and often relaxes the mind.

Guild leadership in MMOs hones the ability to lead human beings (that has no relation to the game itself though).

I like Minecraft, but I'd rather hack Lisp than play video games most of the time.

Protein Folding - http://fold.it/portal/