The limit isn't based on government type, it's based on world size. You can see and set the value in the editor. I think for standard size maps the normal limit is 16 cities. For tiny maps the limit is 8 cities, but I believe Firaxis is going to adjust this in their patch because of some analysis done in this forum that shows 8 is not proportional to map size and other factors. Of course, what happens when you exceed that limit might very well depend on the type of government...
I don't think # of citizens matters, only # of cities. I'm not 100% sure about this, though.
As for what type of win is most affected, I'm not sure it matters. If you have a large empire then the cities on the edge will always have corruption problems because of distance, even with an FP. Thus your 'frontier' cities are mostly for claiming territory, not for production. If you get too
many cities, however, then even your inner cities start to get more corruption and therefor you will lose some production and trade. So any win which requires production and trade will be affected. I think that's pretty much all of them.
The question still remains, how much does it hurt to have 'too many' cities?