If both PCs already have network adapters installed, you are as well to get a "crossover" ethernet cable and network them. It will be as cheap an option as any.
If you don't have a network adapter installed in one/both PCs, then the alternative is "Direct Cable Connection". This requires either a special "Direct Cable Connection Parallel Cable" or a "Null Modem Serial Cable" (not a standard serial cable as used to connect to, for example, an external modem).
There are also special USB cables designed specifically for connecting two PCs by USB for file transfer, but this will be more expensive for a one-off transfer of files. DO NOT connect two PCs directly with standard USB cables.
- burn files to CD/DVD
- USB memory sticks
- temporarily mount your existing hard drive as 'slave' in the new PC to transfer files