So far as we are aware, non-Kingdom/Monarchial systens are in fact possible, but not existant at game launch.

My own group The Free Duchies on the APAC server fully intends to install a City State based Republic as our government type should we succeed in winning a Kingdom in game, in fact.

We are the only such group so far as I know, but there may be others I'm unaware of.

There is technically only one, it's a monarchy.

They have stated that with proper use of the Contract system you can create whatever type of government you wish. At start they will all be monarchies.