well, that depends on a couple of things:

1) is this a "professional" type job? Context matters. I have thrown down my apron and quit in the middle of a shift at a shitty restaurant job myself, but as a well regarded contractor working for a large, well regarded agency these days, I tend to make my leave notices well in advance so that I'm never burning bridges.

2) Do you care about getting a reference from this job for the future?

Oops, I phrased the question badly. I intend to work the two weeks. But I'll be resigning mid pay period. And I wanted to know if people generally are expected to finish out the period.
I've noticed everyone else around here does. Bah!

Yes, it is a professional type job. Yes, I care about references for this job. Double bah!

This is something to discuss with your boss, I imagine. A former coworker of mine gave his notice on the first day of a two-week pay period, and they asked him to leave by Friday, which would be mid-pay-period for us. So yes, it's done.

Pay periods are an artifice.
You work what you work, they give you the fraction of the pay period.

Yes, two weeks is two weeks. I've never heard of anyone insisting on staying until the end of a pay period.

On the other hand, I've never worked in a true corporate environment, and perhaps that's a normal gambit. In my career, it would never happen. Two weeks = 14 days = adequate notice; you're free to leave when your time is up.

I always appreciate more than 2 week's notice, especially for the higher-level jobs which will require a longer search. For those, a month or more is courteous and appreciated. Eventually you get to where you have to plan your departures a few months in advance, so you can prepare and sometimes train a replacement.

But I think the answer is generally no, and if in doubt, ask your boss, but be sure to indicate you weren't planning on more than 14 days.

Ah, okay. Thanks for the clarification. If it were possible I would favorite every answer here.