The single most important running tip I would give runners is to focus on their cadence (how often their feet touch the ground). Cadence is reasonably easy to modify and I believe it has more impact on running efficiency and injury than any other single thing.
Jack Daniels (the coach not the distiller) found that the slower the cadence, the longer you are in the air and the harder you land. (http://ping.fm/UvRn7) Slow turn over means more impact, which causes more injury.
If you take this to the extreme ('Reductio ad Absurdum'), imagine running with just one step per minute. You would have to leap high in the so that you would be in the air for 30 seconds; the landing force would probably break your legs.
So what should your cadence be? It seems that a turnover of 180 steps/minute is right for most people. To start off, check your cadence when you are running by counting how often your left foot touches the ground in a minute, then double the number. If the number is 180, pat yourself on the back and go read http://news.bbc.co.uk. If the number is lower than 180, then you should look at changing your cadence.
There are two ways of changing your cadence. The first is to try to change your cadence and then count for a minute to check the results. An easier way is to run with a metronome, which sets the pace for you. (A running watch that displays cadence is even better, but expensive.)
An example of a small metronome would be http://ping.fm/k2M9f - there are others like this. I trained for several months with a similar device, and it helped me immensely.
To start off, the change in cadence will feel very strange. I remember adjusting my cadence, and felt like my shoes were tied together! My steps were so short and fast that things felt all wrong. It took several weeks to adjust, but when the adjustment did take place, my running improved dramatically. I credit cadence as a key part of my success in going from a 4+ hour marathon to sub-3 hour.