Just purchased and installed a Honeywell programmable thermostat (RTH6350) and for some reason, the furnace just decided to turn on, and it won't turn off - even when i turned the thermostat off!!! There are no shorts in the wires - all was hooked up corectly. Had to power off the entire furnace just to get the heat from turning on. Any ideas??

I would recheck your wiring..... Shut the furnace off at the breaker or SSU.... Then get a pen and pad and write down the color of wires and where it is connect on the Terminal strip at the furnace..

Example: Red wire hooked to R terminal etc They should all match up with the subase of the new Thermostat.
Then go up to the thermostat and Check and make sure the colors match what you have wired at the furnace. R= Power W=Heat G=Fan Y=Cooling C=Common

There are two possible ways the heat could be power on all the time..... You have the white wire or W wire wired to G and the thermostat is set to Fan ON... or the insulation on the R wire and W wire is split and touching each other or they got pinched and are touching together which will make the furnace come on with out the thermostat controlling it..... Good Luck, Its is where I would start first.... there our other possibilitys the control board may of gone hay wire.....