In obstacle people think of some weird and interesting things to do, but these are the basic obstacles..and what I practise at home:
Side passing- Getting your horse to move side ways over a pole, some poles might be straight or in a "L" shape or a "Z" shape.
Holla-hoop(sp?)- Making your horse plant his (front or back) feet in the middle of a holla-hoop and making them pivot around (360 degrees) without moving there one "pivot foot".
The Bridge- You horse goes over a [wood] platform.
Teeter-Taughter(sp?)- Horse goes over a platform that "teeters" (low to the ground)
Water- Horses walk over a tarp
Backing up- Horse may be asked to back up around cones, in an "L" shape or, anything really.
The Cones- Horses are asked to go through (usually at a trot) cones..(weaving).
Hope this helps a bit??
-Kris