I did for a while, but when I ended the relationship I was in at the time, I wasn't going to stick around. Small Midwestern towns like the one I was in are horrible for dating if you're not a nice simple church girl who wants to raise a family with a nice simple church boy. I don't want to generalize too much because I know there ARE interesting people in small towns - but in my experience, most are very bland and family-focused (because most of the people who want excitement and stimulation leave).
Cheshire raised a lot of good points - some other things I noticed...
Internet access was difficult, mostly because of all the trees. You need a good view of the southern sky for satellite, so getting access required a couple hundred feet of cable down the hill (the dish was at the top of the hill). Anything more than light rain would kill the signal, too.
Cost of living was amazing. Rent on the place below was $425/month (and the lake is just below where the image cuts off), and groceries were probably 1/3 of what I pay now in CA (though the difference would be smaller if you accounted for food quality).
Food - Surprisingly, food is kind of a big issue if you like eating well. A lot of small towns have either Wal-Mart or junky little grocery stores...so good produce and "weird" ingredients can be hard to come by. I like to cook, so even spending a few weeks in my rural hometown makes me a little crazy. Restaurants typically suck, too, unless you pick a small town with a decent amount of tourism (like some lake towns).
Design/Style - If you like your place to look good, you may have to build something or do a complete renovation. Most houses in really rural areas are ugly on the inside. That's especially true if your tastes run modern.
Weird Privacy/Lack of Privacy - On one hand, the guy I was dating would regularly walk outside and urinate in the bushes. Nobody saw or cared because there was no one nearby (though I found it a little gross). On the other hand, you can't go into town without people seeing you, talking to you, commenting on your purchases, inquiring about your personal affairs, etc. People would approach with comments like, "You know, I saw so-and-so buying condoms the other day, but I remember Debbie saying her husband had a vasectomy...you don't think she's having an affair, do you? Or maybe she's getting them for her son...oh dear Lord let us hope not. I pray for them, I really do..." The smaller the place and the longer you're there, the less privacy you'll have.
I would consider living somewhere kind of remote again if I were married, but definitely not before that. It's peaceful, but a little too quiet if you don't have someone around to keep you company. I think the ideal, though, might be something that's both rural and upscale (like Napa/Sonoma) where you get the best of both - lots of space + reasonable access to airports, technology, culture, good food.
