What is the furnace brand? Take the door off and see if there is a LED on
the board that flashes while it goes through its sequence of operations, if
so find a trouble shooting guide and follow the instructions.
Have you had anybody work on it in the past? If so, did they change out the
control board or fan motor? Some furnaces when you change the intergrated
control board need a separate wire that comes in another kit, if you change
the board in A/C you wont notice until Heat that you did it wrong. It could
also be caused by someone changing the fan motor and not reconnecting the
ground wire properly.
Could be the negative pressure switch getting weak and not keeping
contact.
If you have L/P make sure it was converted, if not converted, the manifold
may have gotten clogged with ash and the over temperature switch may be
tripped. If you have natural gas don't worry about any frezzing valves or
whatever that guy was talking about.
My guess would be the negative pressure switch, they are easy to check if
you have the right tool.