Turning on the AC for the first time each summer is how you know that warm weather has truly arrived. Chances are, if you inspected and shut down your system properly the previous fall, it will start back up in early summer with no issues. Occasionally though, there's a problem, and it really stinks. The following guide can help you determine the cause of a smelly AC.
Mildew or musty odors
A bit of mildew is perfectly normal when you first turn on the AC, particularly if you live in a humid climate and your AC uses a different vent system than your furnace (or it has been several weeks since you last used the furnace). After running through a few cycles, the HVAC system should clear any moisture and musty odors out of the ventilation system. If the odor persists for more than a day or two, try changing the AC filters; sometimes mildew or mold grows on them during the winter season. You don't want to keep blowing mold spores through your home! If the odor still persists, the culprit is likely heavy mold growth somewhere in your duct system. An HVAC contractor can inspect the ducts and clean out any problem areas.
Burnt rubber odors
Burnt rubber odors mean you need to turn the system off immediately. The culprit is likely to be a belt or gasket somewhere in the fan motor or blower. If you let it continue to run, you risk burning out the motor. You can remove the casing on the outdoor unit and inspect the motor and blower for any damaged rubber parts, and replace any that look worn. Otherwise, bring in a contractor to do the work and make sure everything is back in perfect condition before running the AC again. If there is a smell more akin to smoke than rubber, or distinct metallic burning odor, then you may be at risk for an electrical fire and only an HVAC contractor should address the issue.
The rotten egg smell of a natural gas leak isn't likely with an AC system, since they are usually electric; but you may still get a whiff of something similar to rotting vegetables each time the unit turns on. This is usually caused by dead leaves inside the external unit: you are actually smelling them rot. Remove the outer casing and clean it out, either by hand or with a shop vac, to solve the problem.
Contact an HVAC service for additional help. Professionals like Barnetts Heating & Air Conditioning can offer more information.