The most common complaints that runners have are shin splints and sore knees.

What sorts of Weight lifting will protect my legs.

Shin splints:  Many shin splints can be helped or prevented with
stronger lower legs.  Calf raises are good for this.  You can do bodyweight
calf raises at home by standing on a stair with the balls of your feet near
the edge of a step.  Lower yourself down slightly, then go up as high as
you can comfortably - remember to straighten your ankle.  It is a good idea
to hold the railing while you get the feel for the motion.  Repeat about 20
times, and do several sets.  The machines in the gym will replicate that
calf motion, only with extra weight.
   One thing that is useful for the front of the shin is a silly exercise
you can do at home.  I call them bucket raises, others call them plantar
flexions or shin curls.  Sit on a chair with one leg out in front of you.
Hang a scrub bucket from your foot.  Raise and lower the bucket by flexing
and pointing your foot.  This works the muscles along the front of the
shin.  Put more or less water in the bucket to vary the resistance.  Like
most rehabilitative exercises this should be done heavy enough that you
notice it but not so heavy that you can not finish a dozen or so
repetitions.

   Sore knees:  Most endurance runners have hamstrings that are much
stronger than their quadriceps.  You want your quadriceps to be stronger
than your hamstrings in about a 3:2 ratio.  In addition running does not
exercise the vastus medialus, the muscle that stabilizes the kneecap.  Some
good leg exercises to help this are:  leg extensions, squats, and front
squats.  In addition the turned-foot leg lift described in the rec.running
FAQ is very useful.  You may also want to work with straight leg extensions
and the various leg press machines.  Work your hamstrings to keep them in
balance with your quadriceps.  The best exercises for hamstrings are:
squat, leg curl, standing leg curl, and stiff-legged deadlift.  Be sure to
get someone to show you how to do the SLDL - they can be VERY dangerous if
done improperly.  You can not run with a damaged back.  Remember that
flexibility also prevents knee trouble, so be careful to stretch your legs
before, after, and during your workouts.