Why I was looking at the Wikipedia entry for Rockford Files is a long story, but it did lead me to a transcript of every incoming message left on Jim Rockford's answering machine and after learning the audios aren't available, I found Youtube compilations from seasons one and two.

If someone was so inclined, at least for archival purposes, it'd be great if they could do the rest. The first three seasons stream for free from Hulu, while Netflix has all six.

Note: Someone has copied the transcripts over to Wikipedia, so there's also another source.