Unless you rent an RV, you're going to need a tent. A small tent is great for backpacking, but out on the playa you want some internal space. Keep your gear out of the dust. A big "eight person" tent would be roomy and comfortable for a couple.

This worked fine for me, but could have been a lot roomier. This also works for general car camping for one or two people.

Whether you get something like this or not, do remember your personal hygiene at Burning Man. Nothing wrong with hippie values combined with cleanliness.

And at least a basic camp stove (with fuel). Once again, not backpacking gear, but car camping gear. Comfort not ease of carrying.

One for under the tent, and another for a covering canopy layer overhead. Bring poles, rope, and more rebar to put it up. Most of the kit canopies out there are too weak to survive when a storm comes through. Renting a commercial quality canopy is also an option, think of those things that folks at art festivals have.

Something basic and folding to sit on.

Take a look before you go.

What's being reported on on the ground at Black Rock City.

Smaller and cheaper.

I like these, but do read the reviews, your mileage may vary as some folks find them to be useless.

Leatherman. Obviously handy in too many situations to mention.

So you show up at night.

Bring some plates, folks, knives, bowls, and a cooking pan. Doesn't need to be a camping kit.