Spare Tire
If your trailer hub pattern is not compatible with your towing vehicle, make sure you bring a spare that fits. Even if your tow vehicle has the same bolt pattern, make sure it'll fit on your trailer since some automotive wheels don't have a large enough hole in the center to fit over the trailer hubs.
How do you plan to use the trailer? If you just plan to carry extra gear to the camp site and setup your tent, etc. on the ground, it doesn't take much for "must haves". If you're going to be on some rough roads where clearance can become an issue, you may want to put larger wheels and tires (preferably the same as the tow vehicle if you're going to share a spare) or do a spring over axle conversion. I'm also a fan of trailer brakes (check your state since it may be required regardless). You may also want to pick up a coupler lock if you plan to leave your camp site for long periods of time. I'm also a fan of the silent hitch pin for keeping down the noise and rattling.