Are there any benefits to getting drunk?

It lowers the damage you take (I'm not sure by how much), and also some characters have talents that take effect while drunk, like regenerating health, or doing more damage.

In short, only if you're Logan.

Damage reduction/resistance:
If inebriation lowers damage, it's hardly noticeable. A normal zombie hit would deal about 2.7 squares of health in damage. Caveat: I did this test with three points in Medicinal Purposes, which is Logan's skill that heals when drunk, so the numbers may be a bit off. After one swig, a hit would deal about 2.55 squares of damage. After three swigs, a hit dealt 2.4 squares. So, negligible, especially considering the disadvantage.

Drunk skills:
Medicinal Purposes, Logan's drunk healing skill, has the same healing rate regardless of how many swigs are stacked. Logan's other drunk-benefit skill is Drunken Master, which increases damage while drunk in increments of +20%. I find this impractical. These are the only skills that I know to benefit from drinking.

Drunk healing:
Getting drunk actually does heal you, but only in a certain way. You must drink enough to fall over, which means stacking more than three swigs. You heal two squares of health as you get up. However, getting drunk enough to fall over causes alcohol poisoning, which drains health slowly like drowning. After four swigs, you'll fall over about twice and heal a net amount of three squares.
It's possible to die from alcohol poisoning. Alcohol poisoning health drain rate increases with swigs stack.
Health seems to be a glitchy in regards to alcohol poisoning at the critical level (i.e., four squares of health remaining, which the character heals back up to naturally, if below). Alcohol poisoning sometimes doesn't drain below critical, but I suspect falling over or healing from getting up while drunk may break this gate.

Alcohol can also be used in the creation of the zombie barbecuing festivities known as a Molotov Cocktail.

Tasty, tasty zombie meat.