I live and backpack in the Sonoran Desert. Some of my ten things here are different than my ten things I would pick backpacking in the mountains of Colorado again.

1. Lots of extra water. I hike where there might be no pooled water for miles and miles. Just did it a couple of days ago, in fact. Three of us went in with a minimum of 6 liters each... it was not enough. Heckuva story though...
2. Good topo map. I did not need this so much in Colorado because pooled water was not hard to find there. Here you need the topo in order to plan a relatively easy route to a possible water source.
3. Hat (mine is a very thin, white cotton ballcap) and a triangle bandage (military cravat from medic kit) for shade to the ears and neck.
4. A Lighter (on all of my lists)
5.Trekking poles (on all of my lists)
6. A quality, full tang, fixed blade knife. (on all of my lists)
7. A hiking partner (more important to me here than elsewhere, AND this does not make my pack any heavier!)
8. The ability to disinfect the nasty, horrible, fetid water I do need to drink out here.
9. Knowledge of the area I am heading into. Whether first-hand from a friend or via internet/books.

I could not come up with a 10th item. Oh well.