Is it possible to takeoff without flaps extended? related questions: 


landing wihtout flaps
takeoff with full flaps


My question focus on passengers jets (goes from Embraer E-jet family to  Airbus A380). I don't know why pilots would attempt to takeoff without flaps but lets say they will.

Considering all the other parameters are good enough (no crosswind, long runway, aircraft light enough,...) and the pilots are aware of this unusual takeoff configuration and adapt their action accordingly (including increasing $V_r$ and $V_2$), is it possible for any passenger jet to takeoff and stay airborn (not like the flight spanair 5022) without extending flaps?
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.