Gears are quest items in Epic Mickey. There are four total. Mickey finds the first two on a required quest to repair the Projector Screen to OsTown with Gremlin Markus' help. One used to belong to Pete, but then he gave it to Gilda when he lost a race to her and now Mickey has to beat Gilda's race time to earn the gear. The other one is held by Horace and he will gladly trade it to Mickey if he finds Horace's missing book, How to be a Detective.
The third gear is if Mickey allows Gremlin Prescott to take his wrench back from the Telephone by force. Prescott will disassemble the Telephone, leaving the gear behind. Picking it up will start the "Found: One Gear" Quest. Mickey can then trade it to Laralee at the Museum for the second Power Spark that's on display there.
The fourth gear is in an optional quest if Mickey didn't drop Gremlin Prescott's safe on Moody and repaired Donald. The mecha-mallard will give Mickey the gear and ask him to give it to Moody to help raise his tugboat out of the Thinner River. When Mickey does so, in addition to the satisfaction of helping out the metal substitute of his feathered friend, he will get a gold E-ticket that's on top of the tugboat.