1. Write an email. Let someone know that you're sorry without having to make eye contact, or an attempt at pretending to actually be sorry.
2. Make a phone call. After experiencing the living hell that is answering a ringing phone, whatever you did last night won't seem nearly as bad.
3. Replace whatever you destroyed. If you barfed on someone's cocktail dress, get them a new one. If you ruined someone's relationship, buy them two.
4. Buy a gift. If it's a good enough present, it should get someone to forget about your festive failings, and not stand as a memorial to it.
5. Disappear for a while. You'll get to avoid whoever it is that you want to avoid, and they'll get the gift of not having to see your face.
6. Make a self-deprecating post on social media. Yeah, now everyone knows you're a moron, but at least you didn't have to explicitly admit to anything or subject your hangover to the powerful aromas of a flower shop.
7. Promise to stop partying. Nobody's perfect, so if you're willing to change for the better, someone would have to be Jesus T.H.C. Christ to hold your party past against you.
8. Party even harder. Having fun is kind of your thing, so if you go at it with even more intensity, sooner or later, it's bound to be fun for someone else too.
9. Deny everything. Chances are you weren't the only one imbibing at a place serving alcohol, and if you can't fully remember last night, perhaps someone's recollection isn't all that dependable either. Maybe they got so wasted that they started making things up. Maybe they really crossed the line by coming into work so drunk and incoherent. Maybe they should be apologizing to you.
10. Say sorry in person. It's the most embarrassing option, but that's never kept you from doing something.