Well, there are three types of undereye circles that I'm aware of -- some you can get rid of , some you can't --
First -- most common -- smudgy black circles under the eye from leftover mascara/eye makeup. Even if you take your makeup off before bed (which of course we're all doing) sometimes the solution doesn't get all the coloring agents and they mix with oil on the skin under your eyes and give you raccoon-eyes. Best bet is to try extra makeup remover and face wash first thing in the morning.
Second -- fairly common -- bruised-looking undereyes from sleep deprivation. There are a couple of ways to fix this. One, obviously, is to get more sleep. There are also a number of specialty creams from cosmetic companies that can (with fairly good success, I hear) strengthen the skin or blood vessels or something, make the skin more reflective, I'm not sure -- this helps actually treat the tired skin and make the under-eye circles reduce or go away altogether.
Third -- not as common -- genetic/chronic undereye circles. Yes, I have these, and boy is it fun. Basically, the skin under your eyes is just so thin/delicate that the blood vessels show through and give you a bruised look. You can try the creams mentioned above, but I've never found them to work. Also, if you have fairly deep-set eyes, the shadow from your brow bone will make the already permanennt circles look darker. (If, during the winter, you can ever see any of the veins in your face, especially thinner areas like right under your cheekbone near the hairline, this is probably your problem.)
The best way to deal with chronic circles that aren't caused by sleep deprivation is to find a nice light-reflecting concealer (i like Lancome stuff, myself) and blend it well under and around the eye. It's a little higher-maintenance, but it does work. Or you can just give up and expect that some days people are going to ask you if you're sick, tired, or goth.
Hope that helps -- sorry for the length.
Greekgrrl