P90x is an at home workout system, they bring the gym to your own household with the DVD's!  Knowing most people don't have the same equipment as the gym at home, much of the program uses body resistance exercises (e.g. push-ups, pull-ups) in place of weighted exercises.  However, there are a number of weighted exercises as well.  These can be completed with a set of dumbbells, or with resistance bands.  The pull-up exercises are best completed with a doorframe fitted chin-up bar for your home, though can be modified with resistance bands as well.  Optional equipment is a yoga mat, yoga block, and power stands, which are push-up bars that help you go deeper into your push-up motion.  Another possible piece of equipment is a plyometrics mat.  This is a padded mat that you jump on to lower the impact of the exercise.  I really only suggest this if you are working out in the garage or on concrete.

So to cleanly summarize:

Bare minimum:

-Set of resistance bands.  Having at least three different tensions is preferable.  Click on the link to go to the Beachbody store, where you can buy a set of 3 B-line bands.  For women, they recommend the "standard" set, for men the "super" set.  The "extreme" set is probably not useful by itself, but could be added to the super set for men.

Ideal:

-Chin-up bar

-Yoga Mat

-Dumbbells.  For men, having 10's, 15's, and 20's will get you started.  Dick's Sporting Goods usually has them for cheap.  The 10's might be too heavy for some "fine-tuning" work exercises, but you can always use books from your book shelf!  20's will be a little light for some of the back exercises for sure.  Ideally, you'll eventually want 5's through at least 40's with all the increments, but you can add to your repertoire as you go!

For women, 5's, 10's, and 15's are probably a good starting place.

If you want to buy a set of adjustable dumbbells, I recommend the Bowflex SelectTech brand.

-(optional) Resistance bands.  Dumbbells are advisable, mostly because the form is more straight forward with them, but everyone travels or finds they need to workout in a hotel sometime, so it's not a bad idea to have the bands around for a backup!

Extra:

-Yoga Block.  This actually makes yoga easier, by not having to reach all the way to the ground

-Plyo Mat.  As described above, only advisable if you are working out on a hard surface, like concrete.

-Power Stands. For increasing range of motion in the push-up!  Very ergonomic, one of Tony Horton's favorite pieces of equipment!