These are the three most important items to have when you go trekking into the Mojave desert; water, eye protection, and a hat with a brim or visor.

The hat is a "Boonie Hat" replica, which I frequently wear. It's very useful, as it provides 360-degrees of sun protection, it's light, it has a chinstrap to keep it from blowing away, and the top has an aerated weave to improve ventilation (it allows heat to escape from the top, in arid environments).

Read more about the Boonie Hat here; http://www.angelfire.com/art/enchanter/boonie.html

The canteen is a foam-rubber-padded type, with a 1-liter capacity and a steel mess cup (which I left behind, as I only needed the canteen for it's water). There are also "flexible canteens" which I need to look into, as falling down onto a rigid canteen is CERTAIN to break the canteen, part of your anatomy, or BOTH.
Ironically, it didn't have enough water for the trip (which was VERY short, and we didn't go very far out --- it only got to be about 90 degrees, but the air was devoid of moisture). Because of this experience I'm going to buy a 2-liter canteen (the South African Army uses one, and I'm going to try to get one of those), and I recommend that anyone who's serious about hiking in the Mojave should do the same.

The sunglasses are also very important, as they not only protect your eyes from the sun and improve visibility in bright places, but they also provide protection from dry and/or dusty winds. These ones are "wraparound" sunglasses, so they do all of the above quite well.