Here is my setup. I have cable modem through my cable provider armstrong. I have one computer and one phoneline connected to the cable modem. Here's my question. Can I record phone conversations and have em automatically saved on my computer so I can acces the saved files while away from my house?

Sounds like you are trying to reinvent the wheel. If you have VOIP (Voice Over IP) then you most likely already have voice mail with remote retrieval included with your phone service.

Be sure you understand the legal issues with recording phone conversations. In the USA it is illegal to record a conversation without notifying the other party. "Best Practices", Event viewer, host file, perfmon, antivirus, anti-spyware, Live CD's, backups, are in my top 10

That's not entirely true. While some states require both parties to be aware, there are some states that require only one person to be aware of the recording. http://en.wikipedia.org/wiki/Teleph...

Out of curiosity why do you want to do that. I misunderstood what you want to do. Once you are using a phone the call is really no different than any other call made on a wired land line. So, any equipment designed to record telephone conversations will work. The method of transmission is of no consequence. Once the voice is filtered using the modem supplied by your ISP it becomes a regular call, for all practical purposes. Weather or not it is illegal in all states or not IMO you should still notify all callers that you are recording it.

Federal Laws still apply. It is wiretapping. "Best Practices", Event viewer, host file, perfmon, antivirus, anti-spyware, Live CD's, backups, are in my top 10