If you've followed my tips on prepping a car and race strategy, hopefully you're carrying home some trophies. Aside from that, there's a few more things you'll want to consider.
Obviously you'll need to bring home everything you brought.
If your car is still usuable for another derby (many will last multiple times, especially if they get knocked out for something minor), then you'll be towing it home and there's not much more to think about.
But if you're car is completely wrecked, you have a couple of options. The simplest option (if you have the room) may be to bring it home where it will be available to scavenge parts whenever necessary.
Or it may be easier to just leave it at the derby site, provided the organizers allow it (most will, depending on the value of scrap metal). If you do that, you're going to want to get some of your parts back. First get the obvious things like your battery, gas tank, hoses, and custom wiring. I alway bring a portable engine hoist and if the car isn't coming home, I'll pull the motor and tranny to take with me since I like keep a good running combination. It won't hurt to pull the tires and take them with you if they didn't cut up. I also like to take the front brake rotors, master cylinder, radiator and hoses, carburetor, alternator, distributor, and plug wires.
The main reason is that these are the parts that will often need replacing when you get a car for the next derby, so it's nice to have a stash of parts you can easily swap out at no expense.