Is there any way to get a refund for a game bought from Steam?

This policy has just changed.

Now it's possible to ask for a refund within 14 days of purchase, provided you have played it for less than two hours.

You can request a refund for nearly any purchase on Steam—for any reason. Maybe your PC doesn't meet the hardware requirements; maybe you bought a game by mistake; maybe you played the title for an hour and just didn't like it.

It doesn't matter. Valve will, upon request via help.steampowered.com, issue a refund for any reason, if the request is made within fourteen days of purchase, and the title has been played for less than two hours. There are more details below, but even if you fall outside of the refund rules we’ve described, you can ask for a refund anyway and we’ll take a look.

You will be issued a full refund of your purchase within a week of approval. You will receive the refund in Steam Wallet funds or through the same payment method you used to make the purchase. If, for any reason, Steam is unable to issue a refund via your initial payment method, your Steam Wallet will be credited the full amount. (Some payment methods available through Steam in your country may not support refunding a purchase back to the original payment method. Click here for a full list.)

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Note that Steam's policy has changed - it is now possible to request a refund. The Steam Subscriber Agreement now links to the Steam Refund Policy. Please see other answers which describe this in more detail.

It is possible in special circumstances to cancel an order. I managed to undo a preorder of a game that went on sale the day after I preordered it. I contacted customer support, and since I didn't actually get the game yet (it wasn't out), they allowed me to cancel my preorder and reorder with the sale price. I don't recall whether my credit card had been charged for the initial order, however.

Steam is described as a "Service" in thier licence agreement etc. They hope this will allow them to avoid most online consumer laws in many countries that categorically state that you are allowed a refund in the case that a game does not work.

If you have a technical problem with a game, you can try to get a refund, but I have never tried it.

Steam may refund an entire order if you file a ticket on their tech support site. Note, however, they may require you to have a good reason.

The one time I wanted to cancel an order (when I purchased all 3 Borderlands expansions and then found out two of them include SecuROM), I opted not to cancel mine, because tech support informed me they would have to refund the entire order, and I had purchased some one day sale items on the same order.