Do Not Bring
Burning Man has relatively few rules however there are several things that are absolutely forbidden. If the Gate crew finds any of the following during your vehicle search they will either confiscate it or your vehicle will be refused entry.
Feathers are a nightmare for the cleanup crew. No matter how securely they are attached, the wind will strip bits and pieces off them. Don't be that self entitled asshole that thinks their feathers can't cause moop - all feathers do.
Addendum - Although I don't agree, as of 2013 the ban on feathers has been lifted. Feather boas are still prohibited as they are super moopy. If you do wear feathers - please make sure they are not moopy and don't be that racially insensitive asshole in a Native American headdress.
Although at one time they were allowed, as the event has grown firearms are now banned.
Due to someone being blinded, hand held lasers are now forbidden at the event. as far as I know stationary lasers are still allowed, but must have permits and safety inspections.
If gate catches you with a stowaway, the entire vehicle will be refused entry. Further severe sanctions may also be imposed - I've heard they void all the tickets in the vehicle if you get caught with a stowaway. It is just not worth the risk, so just say no to stowaways.
Although you will see lots of fireworks during the event - they are done by permit issued by the Borg. Larger displays are done by licensed pyrotechnicians with a suitable safety perimeter and safeguards in place. Remember that Black Rock City is a tent city and fireworks done in an unsafe manner could cause a major disaster.
Candle Powered Balloons
Yes, I know these look really cool and beautiful as they float up into the air, but do you really want to be the asshole who caused someones camp to burn to the ground (or worse)? These are a disaster waiting to happen and are moopy to boot.
Although dogs are the only animal expressly forbidden at the burn, it is generally a bad idea to bring any animal. Conditions are harsh to say the least and there are no veterinary services on the playa (probably none within a 2 hour drive). Remember your beloved pet can't communicate that it is dehydrated, suffering, etc... In 2012 some genius brought a cat thinking it would be safe in their RV. I suppose it was - until it dashed out the door and disappeared into the city. I have no idea if it was ever recovered.
Black Rock City can be a stressful enough place for humans - don't be the asshat who subjects their pet to it as well. If the gate crew sees a dog your vehicle will be turned around and you will be refused entry.
Living or dead, plant matter tends to cause immense amounts of difficult to clean up moop. Falling leaves, flower petals, blades of grass, tree bark, and so forth must be removed before the post burn BLM inspection. It does not matter that they are bio degradable - this is a leave no trace event.
Vehicles other than the one you drive in must have a prearranged permit or invitation to pass the gate because driving within the city is forbidden to most vehicles. This applies to all vehicles that are not human powered and without it you will be turned away. I have never brought any other than what I drive in, so I have no experience with this and suggest researching it on the official Burning Man web site.
Note that starting in 2014, the vehicle you are driving will require a vehicle pass as well (these are sold during the ticket sale). The vehicle pass must be attached to the window. I believe motorcycles are exempt from this.