If you are able to ferment in a vessel that can hold pressure, you can use the CO2 production to carbonate.
I did this a few times at the last brewpub I worked at. You need to monitor the gravity of your beer fairly closely. When you hit roughly 75% attenuation, you would then need to seal the vessel. You will also need a pressure relief valve to make sure you do not go over 10-12 PSI (depending on the pressure rating of the vessel you are fermenting in). Once fermentation is completed, drop the temperature down for conditioning.
I have only done this with lager yeast in Unitanks. I was able to open the bottom valve to blow out the yeast to allow the beer to lager with little trub.
After lagering, I would then filter the beer, under pressure, into the serving tank. All this is possible with homebrew sized gear, but it can cost a bit.
The resulting beer does look and taste different than a force carbonated beer. For the most part, the extra effort and gear it requires is not worth it for the "general" public. For the true beer geek, it is nice for a special brew.