Though you've said that you feel guilty, something you haven't really clarified is whether or not you still WANT to be with her. Do you? I'm not trying to justify what you did, but alcohol aside, there must be SOME reason you strayed (I don't judge one way or the other, because I've been on both sides of the fence.). Whether or not you decide to tell her, have an answer to that question before proceeding.
If you still want to be with her, you should definitely build up the courage to tell her what happened, AND be prepared for whatever may come of it. If you tell her and she decides to stay with you, be prepared for her to hold it over your head for God-only-knows-how-long. Don't be surprised if she scrutinizes you every single time you make eye contact with another woman, or makes comments whenever you look in a direction another girl HAPPENS TO BE STANDING in (Granted, trust takes time to rebuild, and even if she may be justified, this'll get old REAL FAST!). If you DON'T want to be with her, I'm kinda torn as to whether or not I think you should tell her what happened.
On one hand, you could end the relationship and NOT tell her you cheated, opting to not kick her while she's down, choosing not to hurt her further than she may be from your ending it. This way, you can do your best to end things on a relatively civil note while you're already on rocky ground and cut your losses without her knowing more than she needs to. However, this runs the risk of her finding out, anyway, and thinking you're a lying d-bag, and she'll resent you for hiding it from her.
On the other hand, you could choose to end the relationship AND tell her of your deed, which will be a huge dose of blunt honesty, will most certainly be met with hostility (her possibly breaking your stuff in anger, breaking you in anger, or saying embarrassing things about you to your friends and family, etc. She may be a lot more reasonable than this. I don't know her.), but you won't be a liar. You'll still be a cheater, though. If you choose to go this route, you might be able to soften the blow by telling her why you want to end it, what you did, and that because you respect and care about her, you want to end it before you do more things to hurt her (Keep in mind, in the heat of the moment, she probably won't see your reasoning until she's had some time to calm down and think about it!).
Whatever you do, if you tell her, do NOT blame the alcohol, because it's SUCH a lame write-off. If alcohol kept us from being responsible for our actions, DUIs wouldn't be punishable crimes. You can tell her you were drinking, but if she wants to blame the alcohol on your cheating, let her make that decision herself.