Ooooo! GOOD question!!!
I've never even tried anything like that!!
I think there is a free audio editor that will let you record things called "Goldwave." I'm not sure its still free (I haven't looked at it for over a year) but if it is, its a good way to go. The documentation that comes with it will describe how to do the recording part.
As for not using a microphone.... Hmmmm....
There is a possibility that you can plug the phone output from the answering machine into the modem on your laptop and record it that way- but I don't know how to make the signal go from the answering machine to the laptop...
If your answering machine has a headset jack, you can buy a cable that will go from the headset jack to the mic input on your laptop. That would work.
If you have a cellphone with a headset jack and you can check your messages by calling the machine, you could plug that headset jack into the mic input of your laptop, call your message machine and record away.
Sounds like a fun bit of technical geekery figuring out how to do that.
Those are my first ideas...
Good luck,
Chris