Adults – Your an adult and should be able to assess your own risk!
Kids – Read the ‘Indoors – Kids Helmets’ post
Factors to consider…
What are the risks?
How valuable is Your Head?
What do the Majority of other climbers in your area do?
Here are my opinions…
Indoor Climbing
Most adults dont wear helmets as most adults know to try to keep head impacts to a minimum. Indoor climbing is a much safer activity than outdoor climbing and the chances something will fall on your head are so small that it is almost negligible. Be aware that climbing walls have to ensure to the best of there ability that everything you use is secure. Also remember you have to sign a waver form for most indoor walls.
Side impacts are much more common on indoor walls. If the climber falls for any reason, the swing effect of being tied to a rope can pull you in any direction, including towards the wall. Ive bumped my head a few times this way and only once did i draw blood.
Using helmets indoors can help you get used to the extra weight you will experience when you climb outdoors.
in conclusion, any head gear that can absorb an impact is good enough to use on an indoor wall.
Good Luck and Happy Climbing 
Clive