What are some good exercises that utilize free weights to increase leg strength?
Squats are probably the most common and are a very effective leg exercise. There are a lot more options that are available to you depending on your weight set and any available equipment.
For a good increase in raw leg strength, you can also do Chair Jumps. Get a (solid, stable) chair, and standing 6" away from it, jump up onto it and back down. This doesn't require any weights at all and is incredibly effective at working nearly every muscle in your legs.