What are some good servos to get started with Robotics projects?

Something else to keep in mind is that there are "digital" servos, then there are DIGITAL servos. What I mean by this is that there are servos out there that are "digital" in that they are controlled by PWM generated by a microcontroller (instead of dedicated circuitry); a good explanation can be found here:

http://www.futaba-rc.com/servos/digitalservos.pdf

...and here:

http://www.servocity.com/html/digital_servo_faq.html

They are programmable, etc - but there is also another type out there (and they tend to be fairly expensive) - these servos use a dedicated serial bus (usually daisy chained), which supplies power and data to each servo (and reduces the number of connections needed to your microcontroller - Arduino or otherwise). They are programmable and definable, addressable, and you can generally get data -back- from the servo (position, rotation direction, and velocity - whether being driven by the motor or by external forces). These are so-called "smart servos".

As an example:

http://www.crustcrawler.com/motors/AX12/index.php

As you can see, they are more expensive, but they do compare favourably against some other standard analog and "digital" PWM servos; when you factor in the bidirectional communications and the single cable daisy chaining - that can make them win out over other solutions.