A trip to the vet last night (routine, not pest related) led to my discovery of something called a "tick twister." It looks like a miniature plastic crowbar. My vet says you wedge the forked end under the tick, pull up while turning counter-clockwise, and the tick literally "unscrews itself." He claims they work great, for pets and humans alike.
You get a large and small model for about $5. Seems like a good thing to keep in the med cabinet. I forgot to pick one up, but I'm going to later this week, as I have to drop off a stool sample (the dog's, not mine).