I don't just mean saving them in my phone. I bought a special recording device that lets me record them from my phone into a recording device. So, I bring them into my Mac and convert them into MP3s.
I started saving my voice mails because they cheer me up. And, I already save every single email, letter, and card that anyone sends to me. But, I don't save every voice mail—only the ones that have some special meaning to me.