I know that there are often summer courses through TAing, but those are much rarer. Many departments don't even offer summer courses.
In that case, are graduate students over summer always supported by RAships? And does an adviser have to have funding in order to support these students (in US)?
Do these standards also vary between professors at public schools and those at private schools? Especially schools that have guaranteed five-year funding?
As Noah mentioned, I don't think there is a binding contract to provide funding.
A few points (US Specific)
Within my school itself, there are variable policies across departments. Certain departments provide 9 month guarantees and if you want to hang around in summer, either convince your advisor to find money for you or find your own. Certain departments guarantee funding for all 12 months, if you take an internship or decide to take a break or whatever, you don't get paid.
If you are an international student, AFAIK, You have two (realistic) options : Convince advisor, get an internship. Finding your own summer funding can be quite tough for international students in the US.
Usually, (at least in my experience), if you are doing good work and your advisor doesn't want to lose momentum, he will get you funding. In my field, it's not hard to get internships even for international students but most advisors will try to get funding so as to not break flow of things. But again, this is experience, not fact.
In my experience in math in the US it is not expected that the school or the advisor provide summer funding. Many people do make money in the summer in a variety of ways, but it's much less formalized than during the year. Personally, I was funded by the NSF half the summers I was in grad school and worked at a summer math program for the other half.
In an engineering discipline, it is not hard to be funded for most/all of grad school. I was a research assistant almost my entire time (at 2 different universities), minus one semester as a TA. Most of the time this was working for grants that my professors had already secured. While TAs may not have as much work in the summer, RAs can work whenever as long as the advisor has money. This works best if you have an advisor who is well-connected and has a large group with several grants from which he can shuffle money around. Newer professors may simply not have available funds for all of their students.
