It depends on terrain, vegetation, water (in all its forms)as well as your activities. I like them when wearing low-cut running shoes. They keep debris (pebbles and twigs) from getting into the shoe tops and keep the socks cleaner.
I've found stretch gaiters made of light-weight swimming suit Spandex to be adequate on the AT, even in several inches of snow. I did not wear them out on my '07 thru-hike. They have no closure and just slip on like socks, then pull down over the shoe. A lace-hook holds the front out and Velcro on the heel keeps the back down. They are light, unobtrusive and hassel-free. DirtyGirl makes something similar.
For heavy trail building/maintenance, I wear similar stretch gaiters made of Spandura, a heavier stretch fabric, over my steel-toe shoes. Again, they keep junk out of my shoes – especially when I'm ankle-deep in loose dirt.
In the Trans-Pecos of Texas such as the Big Bend National Park and the Big Bend Ranch State Park, I use knee-high gaiters made of Carhart canvas with my trail shoes. I think it weighs 10 ounces per yard. After a few washings in hot water – best done before sewing to shrink and tighten the fabric – the canvas provides decent protection from cactus spines,lechuguilla and other assaultive vegetation.
In deep snow where you have to post-hole, gaiters will keep snow from packing into the tops of your boots and will also keep the laces from icing up.