As a mentor I'm looking for someone with the drive to learn and grow, and willing to acknowledge that they don't know it all yet/could possibly learn something from me. It's certainly not that I know it all, I'm reminded daily that is not the case! But if they can't admit openly areas of weakness, you just won't make any progress. The door to learning opens when you can say 'I have something to learn about this'. A protege has to work hard at assignments, but they have to work harder at thinking and following through. Mentoring a protege might seem like child raising, but it's not. If a protege continously drops the ball without making the attempt to reset expectations, things will ultimately fail. Cold hard fact - I'm investing time in someone that in most cases is a gift, I'll never make money from it (or want to), and all I want is to see that time used well.
As a protege remember to think! Move beyond your comfort zone and really think and challenge your mentor during discussions. They are not always right, but they have hard won experience and if you're smart, learn the lessons by proxy where you can. Be patient when your mentor challenges you with assignments that don't thrill you. For example, several years ago I had a protege/employee that had a lot of aptitude, but just didn't seem to understand how to be a good employee. Three months as a team lead with real responsibility quickly showed how painful it is to deal with those that don't complete tasks, don't follow up, don't communicate, etc, etc. It didn't fix everything, but it was a window into the next step, and taught some valuable lessons about how not to be the pain in the ass some of his peers were when he was leading.
Remember that it doesn't always have to be hard core long term mentoring. As a trainer I spend a lot of time with those wanting to learn, and we often have ad hoc conversations about how they might take the next career steps. You might be surprised how much a 15 minute conversation can do to open doors for someone that doesn't see the path.
Finally, I'll add that mentoring works best in person, but that doesn't mean it can't work via phone or email. Just remember that you have fixed resources and that you want to do well by your protege (or two), and not short change them by spreading yourself too thin. Mentoring is a gift, and you get to choose who to give it to based on whatever criteria you want!