No. You need a switch (router) in order to organize and transfer data.
Actually that's not technically true.
Depending on your onboard configuration (most NVidia NForce chipsets support this) if you can get your hands on a Crossover Ethernet Cable, that can support a LAN between two direct PC's, because I have 2 ethernet ports on my PC and used to run my PS3 off of one of them using a Crossover cable when I was living in a place with no WiFi.
No problemo! I have 2 ethernet ports on mine on my onboard NVidia nForce card, and I have my LAN from the modem going into port 1, and a crossover cable coming out port 2 into my ps3, or did before I moved to a new house with WiFi anyway
Incase you're unsure how it works,
Firstly connect all the cables together between the comps with the comps off, boot up pc 2 (not yours) first, then yours, then go to Network Connections, highlight both LAC1 and LAC2, right click on either (with both selected) then click on Bridge Connection, and it links the two connects into internet sharing mode, but it only works with a crossover cable, or ethernet cable & crossover adapter box thingie