I moved from the city centre to a smallish village 3 years ago and have never looked back. Granted, my village isn't completely cut off, as it's about 10 miles in each direction to a city centre and the buses are good, but there's very limited shops in the village, most of which close early, plus close Wednesdays and Sundays. I've rented here since moving and am now in the process of buying, as I'm not planning on leaving anytime soon.
Plus points for me are an excellent, small primary school, low crime rates (plus low house and car insurance rates), lovely community feel and loads of village events (scarecrow festival, big Christmas lights switch on etc), and easy access to open fields if you enjoy walking, which I do. I also love how safe I feel wandering around the village late at night; even the teenagers loitering on corners aren't actually very menacing, and will smile and nod whilst moving out your way, instead of being rude and sullen which is what I'm used to on a whole from the ones where I used to live!
Negatives are very few for me, but you can't sneeze without the whole village knowing about it! This can be handy, as no one could commit a crime without half the street seeing, but can be a pain when you stagger in drunk after a Christmas party
The big downside is the aforementioned Christmas party will have cost £25 to get home from in a taxi, as the buses don't run late.
Overall, I love it and I would never, ever live in a city again.