Here they are, in no particular order:
Your camera will break (or get left at a trailhead or carried away in a river or trampled by a moose).
This is just a fact of life. Under the best of domestic conditions, digital cameras live an endangered life. Get them out in the wilds and in cold, wet, or sticky hands that belong to someone who's been running for anywhere from 2 to 30 hours and it's amazing that they make it back to the car any single time. Which is just to say, don't spend so much on a camera that you'll be disappointed when force majeure separates the two of you. You can be sad that you've lost such a great camera that you'd gotten attached to, but you should never be disappointed because of what it cost. For some people, this will put the limit at $100, for others much higher.
Choose picture quality over most other options.
We're out on the trail with our cameras so we can capture great moments, so you should do so with a camera that takes great photos. In general, this doesn't mean the camera with the most megapixels. It means cameras with great optics and electronics. Apart from testing a number of different cameras, this means spending some time on the web divining from reviews and sample photos where certain cameras in a given price range fall on the quality spectrum.
Be wary of too many moving parts.
With a trail camera, simplicity is often best. Moving parts are just asking to be jammed with dust, mud, water, or exploding gels. I lost a fantastic camera to the red earth of Moab at the 2009 Red Hot 50k when I dropped it in a couple inches of superfine dirt. While it had a soft landing, the telescoping lens mechanism filled with the dirt and stopped fully opening or closing. It was a complete loss. Its replacement has a permanently flush lens, which still has optical telephoto, and I can be a bit more confident that the camera is just that much more field-ready.
Don't be swayed too much by waterproof and shockproof cameras.
The growing number of waterproof and shockproof cameras is heartening for those of us looking for something durable, and they may be good choices for some. Overall, though, they seem to sacrifice too much for the ability to drop them off a tall boulder or dunk them in the local swimming hole. While they are beginning to reach toward the sweetspot of price, quality, and size, right now they just don't seem to fulfill enough of the other important criteria to make them great choices. When buying my latest camera last year, I decided against this category largely for image quality reasons. But the slight bulk, and high cost could easily be deal-breakers as well.
Don't worry too much about size.
Almost any of the current crop of point and shoot compact cameras on the market are small enough to carry on a long, long run without becoming burdensome.
Decide what's most important to you.
Are you an image quality person? Durability? Cost? Size? Everyone has their own special algorithm when deciding what camera to settle on. For me, quality comes first, followed by durability and size - all of which must settle within the "throwaway" price tag of $150 - $200. The great news is that the choices are better than ever, and the starting point is higher than it's ever been. Almost any name brand camera that costs over a $100 will take decent photos and come with some good bells and whistles. Pay a little more and you'll have a bit more flexibility to choose exactly what you want.
Right now I use the Nikon Coolpix S52c, which I've been pretty happy with - taking it on Coyote Two Moon 100k, the Bighorn 100, and a number of training runs. It's fairly small (but not tiny) and true to all the Coolpix cameras, takes pretty nice photos. My previous camera (Panasonic Lumix DMC-FS5) took amazing photos, due in large part to the Leica lens, which was also its downfall in the Martian Moab dust.
Some photos from the past couple of years.