hannah, unless they are very highly skilled (ie. no local people can do the job) and they are planning on living overseas for over a year, I absolutely believe that international volunteers should have to cover their own flights as well as room and board. Volunteering is, by definition, working for free. When I work for pay, a big chunk of my money goes toward shelter and food. So, in my opinion, working for room and board is almost the same as a paying job.
I don't even have much of a problem with overseas projects asking for a small donation. If you honestly believe in what you're supporting, then you'll probably find that you want to support them financially. The truth is that for many of these organizations, money can go much farther than volunteer hours. I DO have a problem with organizations that charge thousands of dollars for a two-week program (not including airfare). In my experience, these projects are usually american- or british-based, and I suspect that much money goes toward overhead.
It is my opinion that any overseas volunteer stint under six months benefits the volunteer far more than it does the program. I think it's a great thing and it can only be positive for everyone in the long term, but I also don't think that cash-strapped projects in third world countries should be supporting international volunteers.
This is coming from someone who has volunteered overseas twice.