If your cities are farther than 10 squares from your capital or forbidden palace (rule of thumb, I ususally play standard or large maps) you'll have pretty bad corruption. Also, if you have too many cities (threshold depends on map size and difficulty level) you'll get more corruption throughout your civ.
Highly corrupt cities can be improved somewhat with courthouses, police stations, and WLTKD.
Note that specialist production is not affected by corruption.
If you really have a big problem with the idea of corruption, you can tweak it in the editor. A lot of people add corruption reducing tags to various city improvements. However, if you take time to figure out how to deal with it as it is, you can dominate with the default corruption rules. Avoiding overexpansion and a keeping your civ pruned back does the trick.