If you recorded your computer’s transmissions from a phone line, could you somehow feed it back to the computer at a later time?
Kinda like recording a TV show.
Depends to some extent on the fidelity of the recording, but as a WAG even if it was pristine I don’t think so as two modems have to interactively “handshake” to communicate, and a pre-recorded bitstream played back via a tape could not respond interactively to the receiving computer’s handshaking inquiries. But that’s just a guess.
I think it depends on what you are trying to do.
Are you wanting to see what your roommates are surfing to on the web? Or do you want to save your x-rated instant message interactions?
Or are you worried that Big Brother has tapped your phone line?
The answer is yes, you could record the transmissions and somehow feed it back to the computer at a later time. However, as Astro said, it would have to be a an extremely high fidelity recording. If the signal was digitized, you would have to sample at 10 times the frequency of the signal. At 56k, that would be 560k, and so on…
Good Luck
-Sandwriter
This won’t work with your typical modem. You would need some slightly more fancy equipment (though decoding the transmissions wouldn’t be very complicated, it’s just that your modem isn’t made to do this). With the right equipment and some know-how, and a good recording, it would be fully possible to completely decode everything sent with the modem.
What kind of equipment would you need? Well, if you knew what you were doing, all you would need is a computer with a decent sound card and a license of MatLab.
Sandwriter, not sure where you got your 10x figure. Nyquist theorem states that you need to sample only at twice the frequency of the signal in order to be able to exactly reproduce the signal. However, telephones only transmit between about 200Hz and 3kHz, so if you record anything outside of this range it won’t do you much good.
Hey, Mr. Blue Sky. 
Playing back the transmissions from your computer’s modem would be possible, but most likely you would not be able to do anything with them (after all, you’ve recorded what your computer said to the outside world, not what it received.) Playing back the transmissions from the other computer’s modem would be possible too, and there’s slightly more of a chance you could get your computer to act on them, but the odds are still good you’d run into problems. In addition to what LtningBug said, you’d have to place your recorder on a “tap” on the phone line; and wouldn’t be able to use a typical “bug” you can buy from wanna-be spy stores, you’d have to record only either transmit or receive at a time. (Disclaimer: IANA electrical engineer.)