I want to control 2 dc motors using the arduino board directly. One motor must rotate clockwise and the other counter clockwise. The directions doesn't change only the speed of each motors. Can this be done without any shield? Them motors may need a higher voltage than the arduino can provide. If I link the arduino board to a power source of about 15 V (the board is arduino mega limits between 6 and 20 ) and I use "analog.write()" function can I output more than 5 volts(the internal voltage)?
Simplest way to do this is two MOSFETs (one per motor, because you don't need to change direction), and some miscellaneous passives, and a flyback diode for each motor.
See this tutorial for wiring diagrams and details.