I pull on the pinions of some of my motors, and there is quite a bit of play. Is this normal, or should I shim them, and where would I get the shims?

Some play is needed. Believe most recommend about 0.75 to 1mm, or 0.030 to 0.040" for 540 sized 1/10 motors. I'd assume a little more for larger motors? Shim kits should be available through most shops, and/or from motor companies.

Thanks!

A little play in and out is a good thing

But you do have to watch for those front bearings going out... If you have any worry about that bearing it is most often worth replacing. The rear bearings do last longer but I would at least check it any time you feel the need to replace the front one, or just replace both, they are cheap it is just not always easy to get into the rear....

I see your point as the pinion is in the front and taking most of the load. I guess the stop and go is very hard on it.