If you have to use serial communications on Windows (that is, you need to connect to the COM1: port), your choices for free software are limited. Until Vista, Windows came with a crappy program called HyperTerminal; even the free upgrade for private use, HTPE for Personal Use, felt like a cheesy Windows 95 program in all ways.
Poking around the lazyweb again, someone says "putty now does serial communications". And so it does! The interface isn't slick, but putty has served the VPNC lab very well for the past eight years on all things telnet and SSH. I can't believe I missed this and have been suffering with a registered version of HyperTerminal for many years.
Oh, and if your new PC doesn't even have a DB9 serial port on the back, USB-to-DB9 adapters are very cheap now. I got this one at Amazon for under ten bucks.