So I've seen it mentioned here repeatedly that Shimano and Campy shouldn't be mixed, but what about the other brands?

Are FSA, SRAM, etc generally Shimano compatible, or is that just another can of worms?

Yes
No
Yes

But it really depends a lot on exactly which components you are considering. Not only by brand but also by series, and road vs. mtn.
Are you serious or are to trolling?

Yeah, it depends on the specific components. I use SRAM chains and cassettes all the time with shimano derailleurs. I also have Campy shifters with a Shimano drivetrain on one bike. Campy 10 speed shifters just happen to work on 8 speed Shimano drivetrains.

Other Campy-Shimano combinations function as well by utilizing various work-arounds and conversion do-dads. Campy and Shimano aren't designed to work together though.

I have a road frame/fork (plus a few other odd parts to work with) that I wish to build up. That was just a question I thought I should know the answer to before I started sourcing any wheelset/shifters/derailleurs/crankset/cassette for it.

Particularly with the hubs and cranks, it seems like there are several other choices out there, and I honestly don't know what issues might arise if say I used a Truvativ crankset with a group that was otherwise Campy Mirage. I was thinking that as long as the derailleurs-shifters and hub-cassette were compatible, there shouldn't be much of an issue putting it all together, but I just wanted to double check.

On one of my bike the transmission combo is -- Campagnolo 10 speed Ergo levers/DuraAce 10 speed cassette/Campagnolo 10 speed R/D and a KMC 10 speed chain. All Campagnolo trans. and all Shimano trans and all Sram trans. as a general rule work best when all the components match. Lately there are several using a Shimano cassette with a Sram trans to get a better feeling trans than with a Sram cassette. Many combos will work. just like there are several degrees of "will work". Mixing shifters & derailleurs & cassette's can be dicy and disastrous so if you have plenty of extra time on you hand try out a few different combos and go for a ride.

Google new zealand wheelworks drivetrain --fantastic calculator for compatibility and a generally informative site

He's probably serious. The question isn't as out of line for a newbie as you think.