Hi TOGA, Buzz here. On the engines i work on, the bleed valves close pneumatically if there's pressure in the duct (so it doesn't leak through a non-working engine). So ever since the DC-8 days we haven't had to manually close the valve before start. Once the engine's running the valve opens up on it's own. (OK, on 727's if you close the bleed valve you can't start the engine) But those swithces are normally left open.
At DEN we had a procedure with the oldest 737's (which had JT8D-7 engines) and DC-10's to do a no-bleed takeoff if the weather was hot (and DEN is at 5200 ft above sea level). It helped a little, the APU would provide cabin pressurization for the first minute or so. But everything since the DC-10's came out has stronger engines and engine bleed is normally left on for takeoff.
And as the others have said, you need a source of bleed air from somwhere to provide wing anti-ice, on the 757 and A320 series ther's a helpful amber indication on the engines screen to remind you to push the thrust knobs forward to provide enough bleed air. Remember, the bleed air is also the air you breathe. Once in a while pilots have forgotten to turn on the bleeds and return to the airfield because the airplane didn't pressurize. It's hard to get them to admit to it, unless we look in the computer that monitors engine performance.
Engine anti ice is "important", got to be careful when you deactivate it (mechanically) and go flying. Many years ago at Christmas time a PeopleExpress 747 was waiting for a new set of fan blades for #4 engine. Seems that the engine anti ice valve wasn't working and they flew through some "fairly moist" clouds. A large chunk of ice built up on the inlet, then broke off and was eaten by the engine. What was left of the fan blades wasn't pretty, about 30% were severly damaged.
Buzz Fuselsausage, Line Mechanic by night, DC-3 Crew Chief by choice.