Lots of chain slack... Time for a new chain? Bad derailluer?
It appears your rear derailleur pulley cage spring is not doing its job. In your picture, it should be pivoted back towards the right side of the picture, maintaining chain tension.

You'll have to remove and clean out your pulley cage, clean up and lubricate the spring and reassemble it. If that doesn't solve your problem, you'll have to replace the derailleur. You can see how to service many brands here: http://www.parktool.com/blog/repair-help/rear-derailleur-overhaul