I'm thinking of building a stash of spare parts for my 87 GT 5sp. What are some common mechanical items that I should have on hand to quickly get back on the road, and even some things I should carry with me in the trunk on long road trips?

A few things that I can think of off the top of my head to keep in the car with you is a fuel pump relay, an ICM, spare fuses, and the tools to change the ICM inside the distributer. I'm sure I'm missing a couple things but I'm sure somebody will chime in and add to the list.

ICM = Ignition Control Module (for anyone just starting out)
I'd also make sure you have some heat sink compound to go with the ICM. Computer CPU heat sink compound will work.
Fuse kit was already mentioned too.

Ignition coil, Cap and rotor is also a good idea.
Fan belt.
Duct tape
Electrical tape
Penetrating oil. PB Blaster or Liquid Wrench are good penetrating oils.
Tire repair kit. (much better than having to use your temp spare that may have dry rotted over the years and you're 200 miles from home). Still have the temp spare just in case, but I'd try to plug the tire if possible.
Basic tool kit.

Cell phone
Cell phone charger
Credit card for emergency repairs (meaning don't plan on maxing out your card on vacation and not have credit available should you break down)
AAA membership isn't a bad idea either.

The fuel pump relay is nice, but not required. There are two on the car.

Either the oil pressure relay or fuel pump relay can turn on the pump. If the fuel pump relay dies, you have to crank the engine long enough for oil pressure to build, then the pump will turn on. However that assumes both are good and you haven't been driving with 1 dead relay for a while. Check them both and if they're both good, that's your spare relay.

I second the AAA Membership. I just had to replace my first ICM about two days ago, at the time I didn't know why my car had just decided to up and die and I didn't know how to change the ICM myself, I'm taking Auto Tech at my high school right now and with AAA they tow your car anywhere within 50 miles at no extra charge. Towed to the shop and my teacher helped me out and she's back on the road. AAA paid for itself just in that case alone for me.

All I carry is a AAA card.

Number one rule for long road trips in a Fiero:
Start looking for gas at 1/3rd tank. (1/2 tank if you're paranoid)
Kit

on a trip to Florida this summer I made sure to take a spare ICM, headlamp, & the standard tools for disassembly (7mm/10mm/screw drivers). Wife thought it was a good idea to get AAA, & we had around $100 in cash for emergency.

I've changed my ignition control module twice on the side of the road while waiting for the tow and neither time it was the cause of my problems. Nevertheless I carry a spare and the tools to change it.

Other than that AAA with a 200 mile tow is my primary tool.