I assume you mean hobby servos, like the one pictured here:
These were primarily designed for RC planes and cars to actuate control surfaces and steering. Continuous rotation is not needed. So a simple and cheap potentiometer is used for absolute position measurement. Cheap pots like this have a large dead zone. Their internal construction is something like this:
And to prevent the motor from reaching the dead zone there is typically some hard stop or peg on one of the gears. Due to the prevalence and cheap cost of these hobby servos, people have found ways to hack them and make them continuous rotation. This typically involves trimming the hard stop and replacing the potentiometer with a pair of regular resistors. Now to get the servo to spin, you kind of need to trick the control algorithm. The pair of resistors make the servo think it is always in the middle of its range (for example). Then you command it to go to some other angle, and it spins at some speed to get there, but since it always thinks it is in the middle, it will spin forever. So what is normally a position command is now a speed command. Voila!
Now the word servo actually applies to any motor coupled with a sensor for position feedback with the required control to go to a desired position. See better definition here. So by hacking the hobby servo to make it continuous rotation, it is no longer actually a servo. That is unless you now add your own sensing and code to servo to your desired position.
But this is a pretty round-about way of getting what you want. So why not just pick a motor, gear train, and sensing scheme to specifically suit your needs? But this is rather advanced for beginners. So you should find some all-in-one real servos. Dynamixels are a popular choice. They are continuous rotation, have real absolution position measurement, are individually addressable, and can be daisychained.
And the LEGO NXT and EV3 motors are also real servos.