If you can afford it, a spare engine. Really hard on your kid when you've worked all week to get the kart ready, then gotten up early and driven a long time to a track, but the engine breaks during practice and the kid doesn't get to race. You can bring some spare engine parts instead (carb, air filter, exhaust pipe, valve springs, spark plug, flywheel key, clutch key, pull starter, ignition coil, etc.) but a lot of times if something breaks inside the block it's impractical to fix it at the track (especially by the next time your class is on the grid).
Even better if you can afford to outfit the spare engine with a chain guard, mounting plate (part that bolts directly to the engine), throttle linkage (so you only have to release the clip in the clevis at the end of the throttle cable) fuel and oil catch connectors (to match your hoses) and maybe even a clutch. The less you have to transfer from the original engine to the spare engine the quicker you can recover from catastrophe.
We also keep an extra neck brace and pair of gloves in the trailer. They can be older / not so pretty pieces - good enough to do their jobs. Seems easy to forget or lose these items - especially one glove!
