Phoenix: I want great and late!
I work at a dinner-only restaurant. One of the drawbacks of working at such a place is that when my shift is done, there isn't much open anymore. Double-Doubles at In-N-Out can only be tolerated for so long, just like any place with a drive-through window or the eighteen kabillion ____berto's 24 hour Mexican joints that dot the Valley. Don't get me started on Denny's, IHOP, or 5 & Diner, puh-leeze. Here's what I know of for a late-night chow fix:
Pita Pit, Tempe: Generously sized pita wrap sandwiches, open til 2 AM, 3 Fri-Sat.
Delux, Phoenix: Ridiculously good burgers, open til 2 AM
Fatburger, Tempe: Not quite as good as Delux, but less costly. Open til at least 1, 2 Fri-Sat
Fate, Phoenix: Decent Asian food, open til 2 AM, 3 Fri-Sat
Boston's, Tempe: Pizza that's a step up from delivery dreck, open til 2 AM, 3 Fri-Sat
Nick's 24/7, Phoenix: Dreck pizza, but the only game in town when you want pizza after 3 AM
Richardson's, Phoenix: Open til midnight.
Are there any late-night essentials that I'm missing?
You can't beat Richardsons one of the best restaurants in town, but since your like me and work in the industry any restaurant open only until twelve is not late enough. Someone mentioned Four Peaks, which besides having delicious brews does have a quality menu for a bar/restaurant. However if you crave a flavorful and sometimes spicy culinary treat with great atomosphere in the wee hours of the morning your best bet is "Fate" and you will not be disappointed. A small little house near central downtown that has been transformed into an artsy, funky little spot serving up some awesome asian fare until 3am.
If you're going to count places open until midnight then Cornish Pasty Co. is open until midnight Fridays and Saturdays.
I've thought the pizza at Boston's much better than delivery, but their pizza gets expensive by just ordering a few toppings (lord forbid you want to make your own pizza) and the restaurant can get way too noisy.
Slices Pizza? Tempe & Old Town. Decent pizza by the slice. Open till 2 me thinks. Good for when you want a $2 fix, not a $10 meal.
Mickey's Hangover. Old Town. Not sure how late they serve food, but they stay open very late. A lot of typical fatty apps, but also salads, etc. Interesting place.
AZ88 - I thought they served late.
That's all I can think of at the moment, but I'm sure you'll notice the trend: follow the nightlife folks!