There is also SE which is a EU form for an AG, and various "partnership" forms that involve a partner that's fully liable. Usually, that partner is not an actual person but a "legal person", i.e. another SE or GmbH.

Even if you're not listed on a stock market, you might want to take on investments, e.g. "give me 10 million for 5% of the company" and I assume the latter is much easier with an AG.

Here in Sweden we have A LOT of companies own and operated by state and local government and they’re all “aktiebolag” which literally translates to “stock companies”. For smaller businesses you can register as a sole proprietor and some other odd structures if you are a group of people. You’ll often see the same thing for non-profits as well.