If you just don't like the game, you're not likely to have much luck. If the game is actually buggy, so that it's impossible or very unpleasant to play as a result, you're a bit more likely to get your money back. To improve your chances:
- Be excruciatingly polite. People in service-type jobs get yelled at a lot, so politeness goes a long way. If they initially refuse, don't raise your voice; just make your case calmly and clearly.
- Rehearse your points. If the box says (for example) "Multiplayer action!" but the multiplayer feature is buggy and doesn't work, point it out and explain the problem.
- If the copy-protection is such that you can't play the game without the box contents, e.g. the CD, explain that clearly as well so that it's clear the return means you can't play the game anymore. But I'd only bring this up if they raise objections to the return.
In the US, the Uniform Commercial Code says you're within your rights to get your money back if a product doesn't do what it claims to do. It also says EULAs (e.g. "THIS GAME SOLD WITHOUT WARRANTY blah blah blah") are not likely to be binding, since the warranty disclaimer and/or EULA isn't visible at the time of sale.
Unfortunately, there's been at least one prominent case where a court sided with Blizzard on a EULA, so the law may be becoming unsettled on this matter.
And IANAL, of course. But you can read a book called Bad Software by Cem Kaner to get an idea of what rights you have with poorly-performing programs. You have more rights than you'd think.
EDIT:
While it wasn't a game, I have gotten my money back on bad software before. I bought a personal finance program for my Palm handheld some years ago. It was buggy. It would often show wrong amounts, and when an account had an even amount (like $50.00), it would crash. I worked with the company to try patches, hoping they'd fix the problem, but two or three patches later, the bugs remained. Finally I'd had enough; what use was a personal finance program that couldn't even add correctly? So I politely informed the company that while I'd tried troubleshooting and patching, the problems weren't getting fixed, and I asked for my money back.
Their response? They gave me my money back right away (credited back to my credit card), without any argument. And I went and bought a different program that worked, and that I use to this day.