There are alternatives to DEET that work well (according to independent testing). Several years ago (at least) there was a study written up in, of all places, the Wall St. Journal that compared different non-DEET alternative repellents. The winner at that time was a spray with 30% lemon oil of eucalyptus (aka Repel) - worked as well as 21% DEET, if I recall correctly. I've used it, and it works quite well for me in heavy mosquito times in the Sierra Nevada. Before that article, I was using the runner-up (a product called Bite Blocker) which is made with derivatives of soy oil; I used it in SE Alaska as well as the Sierra, and it worked well for me. I do find I need to re-spray every couple of hours, but that's not a big deal for me.
There is a newer product made from something originally extracted from tomato plants; it's called BioUD and marketed by the same folks who made (and still make) Bite Blocker. According to its literature it lasts longer than DEET and is as effective. When my Repel runs out, I'm getting that: http://www.homs.com/
The lemon eucalyptus product is called Repel:
Don't bother using other "natural" products other than those 3 I mentioned; only those ones have done well in independent testing, citronella and others really bombed in the WSJ article.
I spray face, neck, hands, socks, and any other exposed skin, as well as my hat brim.
I second the vote for Peter Vacco's headnets when the mosquitoes are really swarming; they are SO much better than any others because it's easier to see and breathe through them.
Woven nylon pants and shirts (you can find plenty of those at Sierra Trading Post or any outdoor retailer) are also a good line of defense.