Do all Bitcoin alternatives need to have a coin limit? In the Netherlands, it was just in the news the e-gulden was launched.
Before we got the Euro (€) we had that currency in our country.

An E-gulden (EFL) is currently 50 EFL = €1,50

But is there for any cryptocurrenty a limit? Or could the creators just create as many as they like? 

I know that Bitcoin has a maximum coin limit.
E-Gulden has a limit of 21 Million.

Most, but not all cryptos have a limit, for example DogeCoin recently announced that there would be a minimum reward of 10,000 doge for every block after the previously announced reward schedule was supposed to end.