Good answer, but you did not answer the OP's origional question below:
Can you do this with a continous rotation servo? ...tell it to turn to 45 degrees and stop there for instance?
Actually, both methods allow that. Any unmodified servo is capable of going to 45 degrees and stay there if you continue supplying the pulses for that position. It will not stay there by itself.
With the first method I showed, the servo has a 360o
magnetical sensor with a high resolution and it has a built in microcontroller. You can tell the servo to go to ANY position and stay there. Or to just rotate continuously. The way the magnetic encoder works allows the servo to stop at 45 degrees even after a random number of complete rotations.
The second method I showed, is a servo hack, and because of the way the potentiometer is built, you can tell the servo to stop at any degree between about 270 degrees (the range of the potentiometer resistance), for the rest until 360 degrees it is unresponsive. But, there are 360 degrees potentiometers out there (minus about 2-3 degrees), easy to replace the original one. Just look at the video and you will see the servo rotating continuously and then stopping at a certain degree and staying there until a new position was issued.
Of course, if you buy a continuous rotation servo and do not modify it, you can't tell it to go to 45 degrees and stop there!