The air being blasted into the room by your air conditioner should be odorless. It's chilled, filtered, and enters the room via the unit's vent. When that air has a noticeable smell, it's a call for action, because something is clearly going wrong inside the unit. All smells are a call for action, but some smells are a cause for concern.
A Musty Smell
When your air conditioning system emits cool air that smells musty, like a room that needs to be aired out, the cause is probably pretty minor. AC units feature filters, and these are designed to trap dust, allergens, and other airborne irritants before they can enter the room. Filters need to be cleaned, and an accumulation of dust can lead to that musty scent that you're experiencing.
The unit's filters are located behind the wall-mounted vents in ducted systems and in the primary wall-mounted component of a split system air conditioner (which should feature a large panel that flips upwards to reveal the filter). Carefully detach the filters, give them a good wash in warm water (with mild detergent), and then allow them to totally dry. Once they're reinstalled, activate your AC again, and that musty smell should be gone.
A Moldy Smell
A moldy smell escaping from your AC isn't cause for alarm, but it's more serious than a musty smell. It can indicate the accumulation of moisture inside the unit. This moisture should be dissipated via the standard operation of the unit. The unit's outdoor component features a primary condensate pan, generally located below the evaporator coils. This pan should be drained into a drain line. The pan or drain line may be clogged. Contact a qualified air conditioner technician for repairs. The unit's internal ducts may also need to be treated for mold.
The Smell of Smoke
A smoky scent coming out of your air conditioner is concerning. There may not be a fire inside the unit, and it's likely that a moving part (such as the unit's fan belt) has worn or moved out of alignment, creating a dangerous amount of friction—and a small amount of smoke. There's a risk of fire, so you should immediately deactivate your AC. Have the unit inspected and repaired as needed.
A Sweet Smell
A sweetly caustic scent being produced by your unit is unexpected, but can in fact be dangerous. This sweet chemical smell can be the result of leaking refrigerant gas inside your unit, and this is a real problem as this gas is toxic. Do not use the unit again the source of the leak has been identified and patched. The unit may need additional refrigerant to replace the gas lost due to leakage.
Any curious smell from your AC warrants investigation, but some are riskier than others.
For more info about air conditioning, contact a local professional.