hi,
if I use arduino along with a visual motion sensor and motors/servos, could i get a door to automatially open when the motion sensor detects movement? (could also use an ultrasonic sensor?)
technically yes, but you would need a really strong motor / servo.
I guess that there are other options for opening doors ?
counterweights will dramatically lessen the load on the motor, consider using them in combination with a pulley system.
Sure, most garage doors are automated these days so the concept is simple, sensors and the final control element, the door opening mechanism.
However the mechanical part of the door opening is not straight forward. Does it have to turn the door knob first? Does it still have to work manually in emergencies or if power fails? how much space is available around the door? What power is available at the door? etc, etc, etc.
Lefty
wow, lots of ideas,
truth be told, all i wanted it to do was open my bedroom door when i walked near it lol.
could a hydrolics system work? that way it could be mounted at the edge of the door (non-hinge-end) and need less power to open the door?
I only want the door to open, not close
If you only need to have the door open then why don't you look into spring loaded hinges or attachments. Once closed and latched a simple solenoid could be activiated to release the catch and spring power would do the rest 
Lefty