Is it possible to takeoff without flaps extended?
Yes take-off without flaps is possible. The Airbus A300 and Boeing 767 are approved for such take-offs and it is being done regularly. It results in a better climb gradient, especially with one engine out. The one engine out climb gradient is an important and sometimes limiting factor in take-off calculations. 

One important constraint is the length of the runway.

Another limitation, perhaps less obvious, is the maximum rolling speed of the wheels. The tires are rated to a limited speed which may be exceeded by a flap-less take-off.