I found that the Mountain Laurel Designs short gaiters linked to above work very well with my Montrail Hardrocks. In fact, they stuck well to the shoes even without using the cord under the foot. No gaiter will cover the area over your toes, so you can't expect dry feet.
My first extended backpack with trail runners instead of boots was this August in Wyoming's very buggy Wind Rivers. I found out the hard way that I should have worn gaiters all the time. When I'd sit down, my pants would ride up enough to expose my ankles. Smartwool socks do not keep off mosquitoes! I spent two weeks gritting my teeth and trying hard not to scratch. I read somewhere that if you don't scratch them, the bites won't itch. I have never been able to test this theory (which sounds like folklore anyway), since I don't have that much will power!
Except for the mosquito bites, I found that the trail runners actually give me more support than boots ever did. Thanks to my dog's getting sick, I was carrying most of his load as well as my own, and I know that with the added dog food and water my pack was over 30 lbs. I never once missed the boots!