I'm from Canada. In most countries I can stay for up to three months without needing a visa. I was reading information about the Schengen agreement and how it essentially eliminates borders between all participating countries.
Is it at each country's discretion?
In the Schengen Area, you typically can be there for 90 days out of 180. The trick is that Schengen acts like one country - no matter how many countries you visit.
If, for example, you enter Norway, stay for a month, then Sweden for a month, and then into Germany for a month, you're done for the next three months. It doesn't matter how you allocate your time amongst the countries, you get 90 days out of 180.
Countries adopting the Schengen protocols agreed to this common term, and do not have the discretion to make their own rules. Indeed, this is partially why Ireland and the UK opted out.
Rules regarding visas, entry, stay and residence are in principle at each country's discretion and do in fact vary quite a lot. Many countries also entered reciprocal agreements by which they commit to treating each other's citizens in a certain way thus foregoing some of their ability to set those rules at their discretion.
Members of the Schengen area in particular essentially transferred this competence to the European level and agreed to a common set of rules laid out in the Visa code and the Borders code. The system leaves very little discretion to each individual member state.
Some older members like the UK got an exemption and will most likely never become part of it but entering the Schengen area is more or less mandatory for new members of the EU (so very little discretion there as well, if a country wants in, it has to commit to becoming a part of the Schengen area down the road).
