Some of us are reluctant to provide public lists of the free authenticated e-mail servers that we know of to prevent the riff-raft from taking them over. But be sure there are many of them. And even the free ones are usually passing the hat to cover operational expenses.
One I use has been far more reliable than any commercial ISP that I have used, and their configuration is not even in the minimum fault tolerant configuration that a commercial operation would be in.
QSL.NET offers free agressively spamblocked e-mail reflectors to Amateur Radio operators, but not a mail server for outgoing mail. One may be available on a pay per use, but I am not sure about that.
-John
Personal Opinion Only