sounds like an intermittant switch or relay or a bad thermostat. There are two terminals in the typical 4 wire thermostat that if you short accross them and it goes on and off like it is supposed to then it is the thermostat. Otherwise sounds like a service call.
The november issue of family handyman has an excellent article on cleaning your own furnace. It could be a dirty ignitor of in that area but be careful cause one type can be broke by touch or jarring.