Um, the answer is actually "it depends". First, what word processing package did you have on your old PC? Was it Word and was it part of a full Office package, or did it come as part of the OEM bundle? If the latter, you can't install it on a new PC: the licence is for the old PC only. If however you've got a full copy of any version of the Office suite, you can probably convince Microsoft that you've taken it off the old machine and want to transfer the licence to your new one.
Vista does have a rudimentary word processing function in Notepad, but it's nowhere near as full-featured as Word. If you can't transfer your old version to the new machine and you don't want to shell out for a new copy of Office, try Open Office click here which is free and produces files compatible with Office.