If you have multiple NICs, theoretically you should be able to run as many simultaneous connections as you have NICs.
This is quite popular actually with mobile computer users, who will often use two wireless APs and NICs from the same machine. (i.e. built in WiFi card for Internet and a PCMCIA or USB WiFi adapter for scanning / packet capture... i'll leave the purposes of that up to the imagination). I've setup a desktop with multiple WiFi adapters using the PCI bus wireless card + cantenna and a USB Wireless-N adapter and can connect to different wireless APs simultaneously. Laptops are usually the preferred platform for scanning / walking across multiple wireless APs simultaneously while utilizing multiple WLAN adapters.
If you have two of the same NICs, you can bridge the connections, to create a single connection with the bandwidth capacity that is the sum of the two connections - which could boost performance for online gaming, downloads, uploads, etc. I believe there is also a way to bridge a wired LAN connection with a WLAN connection, but i've always been in situations of using a wired LAN at work and WLAN from home, so i'm not sure how that would work without software to control it. WLAN is the only method i have used to successfully run simultaneous connections.
Edited by Cyb3r_Ninj@, 13 December 2007 - 11:34 AM.