This article is from the Running FAQ, by Ozzie Gontang with numerous contributions by others.
I think the consensus in the various posts in rec.running is that
treadmill running is very similar to outdoor running. The physiological
effects of a person moving relative to the ground vs. the ground moving
relative to a person are not greatly different. Certainly there are some
biomechanical issues involved, notably the tendency for the treadmill belt
to slow down momentarily during each footstrike. Many treadmills have
compensatory schemes to minimize this effect, including large flywheels and
microsensors which constantly adjust the belt speed.
Some differences between treadmill running and outdoor running are the
absence of wind and visual motion cues on a treadmill. The lack of wind
makes sweat generation a serious issue, and a strong fan blowing directly
into your face is almost a necessity for serious training. The absence of
a headwind also gives a slight speed advantage to treadmills, and it is
often suggested that an incline of 1 to 2% on the treadmill will compensate
for the lack of headwind. The lack of visual motion cues on a treadmill
can be disconcerting initially, but this is something you get used to. It
may contribute to the feeling that you are working harder at a given pace
than you would outdoors.