Equipment
Unlike many sports, running doesn't require a lot of gear. The two items that I regard as critical are shoes and GPS watch.
Shoes
As I mentioned elsewhere, I'm completely sold on minimalist running. That means shoes which come as close as possible to the experience of barefoot running. In the warmer months, I run in Vibram FiveFingers, which look like gloves for your feet. All there is between the soles of your feet and the ground is 4 mm of rubber. They feel absolutely terrific to run in. I completed the Bristol Half Marathon in a pair of these.
Vibram FiveFingers Bikila
In the winter I prefer something a little warmer. My choice is the VivoBarefoot Evo which has a sole not much thicker than the FiveFingers, but looks more like a conventional shoe, so you can wear socks inside them. I completed the White Horse and Henley Half Marathons in these, and I plan to run the London Marathon in them too.
VivoBarefoot Evo II
GPS Watch
I've found a GPS watch to be absolutely indispensable. It tells you the elapsed time, how far you've run, your current pace, your average pace on the run so far, your current heart rate - everything you need to know not only to manage each training run, but also to manage your pace in races.
The model I'm using is a Garmin Forerunner 310XT. Brilliant piece of kit.
I upload details of each run from the Garmin to my PC and store them using a software package called SportTracks. This keeps a complete history of my training and races, and can display all sorts of charts of pace, heart rate, elevation etc as well as showing each route on a map.