How many defenders do you keep in your citys? I find that if the AI manages to even get next to your city in the first place, you're in trouble already since all your improvments, towns in particular, get sacked. Yes you do have a massive cultural + city defense bonus, but is it worth losing 3 towns over? I normally only have at most 2 defenders in a city and more defenders in trees and hills inside the edge of my cultural borders. I'd rather lose a few more units than a few towns.

What do you people do?

I keep most of my defenders inside the city, because i fear sneak attacks. I care to keep a road network in my city radius, to attack enemy troops before they get to the city. I hold in the city different units, and some collateral units, so i can deal with almost every unit i can encounter. If an attack comes to my border, i always try to soften it up using cats/cannons/artillery. This is a time-saver and, you know, time is everything in war. As for towns, i rarely have plenty of them in a border city, because it's likely to be one of the most recently founded, and it doesn't have many improvements, so i don't really care about them. I've tried to use decoy armies once, and it did work for me: half of the enemy stack reverted to the city i pretended to attack, and i finished off the remaining.
I tend to keep units rather than improvements: units are precious, and the more battles they win, the more they get stronger. Rather than letting the enemy wipe out 4-5 hill units that don't get city support, i would lose a cottage or two. They can be replaced at no cost, units require hammers, and veteran units are a pain to lose.

Normally I will keep 2 units in a border city and 1 in every interior city. Whether I have more units depends upon whether I am going to be a warmongerer or not. If not I will concentrate on getting my cities built up and keep an eye on my neighbors, plus any of the insanely aggressive Civs. Monty, Caeser and Issy, as examples, will come looking for you from across the world. So I try to make sure that my overall power rating does not slip too far.