If your motherboard has two NICs, connecting both of them to the router will achieve no speed increase in either the internet or network transfer speed unless your router supports link aggregation and properly configured on the NIC side. You can however, connect one NIC to the router for internet and another to a second desktop to create peer to peer network.
Actually, you could use this with a Virtual PC session to browse with and let the physical adapter carry all of the download / upload traffic. But, you are gonna hit a cap in your router (who knows when... depends on your ISP speed / router MHZ, adapter speed, etc...) I think it would be of more use to you if you wanted to run a *nix OS as you can do some really useful LAN segregation and intrusion detection with two NICS (this can be done in NT-OS's as well, but requires a lot more vigilance / attention to detail IMHO that cannot really be justified due to the availability of free utilities on the "other side" and a deep base of knowledge and experience in doing so - at least in Fedora Core land) Also, could be good for setting up a routed subnet (using your primary NIC as a gateway) in the event that you have a teenager with wandering eyes that you would like to keep an eye on... [EDIT] Actually, the whole routed subnet thing is pretty much gonna be the only way to take advantage of anything I mention - unless you wanna start dicking around with LANACFG (*looks for barfing smiley...*) [/EDIT]
the process of using 2 NICs on the same board for load balancing is called "teaming" you can't do this with consumer level motherboards, you need a server motherboard to do this.