On my dirt bikes (Kx500, Kx125) I'll shut the fuel off when tailering, storing, removing the tank or I'm done riding for the day. When I stop to take a break, I'll leave it on (one of the guys I ride with shuts his off everytime we stop...seems to always forget to turn it back on). I'll also shut it off if I need to lay the bike over and can't remove the tank. I'll also shut it off and run most of the gas out of it. If it's going to be more than a few days beforre I will run them again...I'll drain the float bowl.
On my snowmobiles (700XcSp, 600XcSp), the fuel gets shut off for storage only. Even then I shut if off...run the carbs dry and drain the tank. Other than that it's always on.
My street bike (Cbr1000) always gets left on, unless I'm putting it up for the winter. Then again it's shut off, run dry and drain the tank.
The sleds and bike have a vacuum fuel pump, so fuel shouldn't flow to the carb without the motor running/turning over. The dirt bikes rely on gravity to fill the carb. If the float is sticking or out of adjustment it'll keep running.