Yes. If you are talking about sprinting.
Speed is determined by your ability to propel your body forward relative to your bodyweight, the harder you push into the ground the more force you get to propel your body forward.
If you get stronger legs, you can put more force into the ground however your bodyweight will act as resistance against that, so it is important to get as strong legs as you can while gaining the least bodyweight you can to run as fast as possible.
Plus, it would be silly all these olympic sprinters doing all those heavy squats, cleans, snatches and deadlifts if it did'nt improve their speed.
To do this you'l want to train for pure strength without an emphasis on building muscle: keep your volume and reps (stick around the 1-5 Reps per set) really low to stop adding so much bodyweight (below 25 overall reps per exercise, so if you did 5 reps per exercise, stick to 2-3x5) and do not use maximal weights but use heavy weights(80+% of your 1RM and never train to failure). Take more rest between sets and hit the weights more frequently. Stick to freeweight compound exercises(Squats, Deadlifts etc..).
You can read more about this sort of thing here>
http://www.askscooby.com/excellent-postings/basics-of-pure-strength-development-17059/However, your feet should only remain in contact with the ground for a very little amount of time so this force has to 'explode' repidly into the ground every single stride you make, which means it is important to work on explosiveness as well which means lots of plyometrics (Vertical Jumps, Bounding, Box Jumps etc..) and consider using more explosive exercises (Clean and Jerk, Snatch, Push Press, Box Squats etc..) Be sure to have a competent and qualified person teach you some of these more difficult lifts.
There is also a good article that explains it more thoroughly here>
http://www.dragondoor.com/articler/mode3/269/Technique is also very important in sprinting too, but I don't know much about that. You'd have to speak to a proper coach on this, it can take years for some athletes to clean up their form. A documentary I saw the other day about Usain bolt showed fallacies in Usain's sprinting form (if he corrected this he could go even faster :O ).
On top of that, because stride speed x stride length = Running speed, you can increase your running speed by stretching your legs out so you can get more stride length too. Be sure to include dynamic stretching before working out and static stretching afterwards.
If you are talking about distance running. That changes the ball park completely.
Endurance is hindered by strength, if you get stronger the chances are your endurance will decrease. So it is best for these athletes to stick to running, running and more running for their training. They could, however, do weightlifting but do much higher rep ranges than in the 'strength training' areas such as 20+ reps per set with not very challenging weights.
