Is there a limit to the number of telephones I can have hooked up to the same line?
Yes and no. There really is no absolute limit on the number of phones or devices. Your phone or device has a label on it that states either a value called REN or ringer equivalence. There is a limited amount of power available from the phone company to make your phones ring. In other words, if you have too many phones, none of them will ring. Your callers will think your phone is ringing (they won't get a busy signal), but you won't hear any ringing!
Though the limit is around 5 total devices, you will know if you exceed the limit because the phones just will not ring anymore. If you call the phone company, they can give you your system's REN limit. Then, add up the REN of all your devices on the line. If they are less than the REN limit, you are OK, if you exceed the REN limit, your devices may not respond to the ring signal.
Most phones have a REN of around 1. Computer modems, fax machines, and answering machines also have a REN value, and you should take them into account when figuring your total REN. I have a US Robotics Sportster Voice Faxmodem, and it has a ringer equivalence of 0.4. My answering machine also has a REN of .4.