I would recommend good quality wax cotton jackets, such as Barbour and Filson. I know some people seem to think they aren't breathable but I would say I get no wetter from sweat wearing a Barbour than I do when wearing Gore-Tex and such like. Also if you match the outer layer to the weather/activity you will be much more comfortable, I find if I use my waterproof only when it is raining, I remain much more happy.
I think wax cotton is the same as most things though, keep it clean, look after it, and it will breathe ok, clog it up with dirt or shoddy reproofing, and that is when you get problems.