I've been running since some twenty years, with a forefoot strike. Usually we use a heel strike while running or walking, but I learnt this way of running when I started Taido, during warmup but also for long distance run.
The forefoot strike is usefull to reduce the impact on the ground because it uses more joints and muscles (phalanges, arch and ankle) thus allows you to run barefoot even on hard surfaces.
Since more than a year I also started to use so-called minimalist shoes (like the Vibram Fivefingers or the Terraplana Vivobarefoot) with a very fine sole (2 or 3 millimeters), no arch support and no cushion for the heel. These kind of shoes gives you a feeling very close to barefoot without risking to hurt your feet or get them dirty.
This way of running seems to be natural among people who don't use shoes daily, and it's also being more and more popular among runners.
Some researchers started to study this way of running, to compare it with heel strike running and to question the design of current running shoes with arch support, thick sole and heel cushion.
Here is an article about barefoot running and a comparison between forefoot and heel strike in running by Daniel Lieberman from Harvard University:
For more infos about barefoot running and minimalist shoes, here is an excellent site: