For just 2 machines, you could use
Direct Cable Connection, calling for no hardware beyond a bi-directional serial cable. (See also, Microsoft:
How to set up a Direct Cable Connection in Windows XP)
For the more common, and more flexible, standard home networking setup, both machines need a network interface of some sort; cheapest is an ethernet network card, but there also are USB network adapters which do not involve opening up the machine. If just 2 machines are to be involved, using the ethernet approach, you will need an
Ethernet Crossover Cable, something different from a standard ethernet cable. Be sure you get the right cable for your application.
IMO, the best way to go is ethernet, and to employ an intermediary device, such as an ethernet hub (cheaper) or an ethernet router (a little more expensive, but more versatile) through which to connect the machines (using in this case a standard ethernet cable). With hubs and/or routers, along with ethernet cards in the machines to be networked, a considerable amount of flexibility and expansion capability is afforded, including among other things networked outboard data storage (independent, stand-alone external drives), networked printer (or other peripheral) sharing, and of course easily connecting multiple machines to a single broadband interface. A USB-based network can, depending on the equipment involved, be just about as flexible and scalable, though limitations likely will be hit earlier.
Finally, if you do go the ethernet way, consider a wireless router; you may not need it yet, but odds are you'll want one eventually, particularly if you pick up a current-production laptop or handheld (many if not most now have built-in wireless support), or decide to go with a VOIP Internet Phone, or want to incorporate your computer network into your home entertainment system. A wireless router is not all that much more expensive than an older-style conventional wired router, and most actually are dual-use, that is, they offer both wired (ethernet) and wireless (WiFi) connectivity, permitting the simple connection of both wired and wireless machines to the same network. Wired or wireless, my recommendation would be to base your network on a router - you'll be glad you did as your needs grow. And trust me, your needs will grow.