I would like to play this game, however I don't want LEGO pieces/sets all over the place! Is it possible to buy just the game without any LEGO pieces?

I see the game all the time used for as little as $10, but you literally can't play through the game without the base (which plugs into the USB) and figures!  

You do need the LEGO pieces to play the game, but just to beat it you only need the base characters. If you want 100% of all the gold bricks and minikits, etc., you'll need other characters, although the game is nice and will let you 'Hire-a-Hero' for a certain amount of studs and giving you temporary access to a character you don't have. Alternatively, you can just pick up a few characters with tons of abilities, like Marceline from Adventure Time, who effectively makes several other characters obsolete.