While sleep really is the best solution for dark circles and eye bags, there are other ways to combat these without opting for expensive treatments. First, we have to differentiate under eye circles from puffy bags. These are really two different things: dark circles are caused by lack of sleep and dehydration while puffy eyes are usually brought about by water-retention or allergies (eating too much salt, alcohol or simply, fluid build-up).
Quick solutions for dark circles: regularly apply eye cream with retinol, Vitamin E or caffeine and blend a light-reflecting concealer (one shade lighter than your skin color) on your under eye area.
Remedies for eye bags: apply a cold spoon on the area (or any cold compress), place good old sliced cucumbers on your eyes for 15-20 minutes or put teabags brewed in milk (leave to cool in refrigerator overnight) on eyes for 15-20 minutes.
* I just wrote an article on this for LOOK magazine (July-August 2012 issue). To read more about it this and to get more tips, watch out for the magazine. Will keep you updated!