You can use two connections in one Windows machine, but you can't use the full bandwidth of both connections in a single download because the server at the other end will only respond to one IP address so, as both of your internet connections would each have their own external IP address, you'll only get a response from a given server down one connection at a time.
All is not lost though! As other posters have mentioned, you can use multi-WAN routers to load-balance connections (so two simultaneous downloads would be split across the two connections, for example) but on a Windows PC with two network connections you might be able to use this.
My apologies! I linked the Windows 2000 article. Rather than search for the Windows 7 one, I've just gone and tested it myself - go to your Network Connections list and for each of your two network adaptors, right click, choose "Properties", "Internet Protocol Version 4 Properties", "Advanced", then uncheck "Automatic Metric" at the bottom and enter 0 for each one.
Windows will now treat both connections equally and randomly assign sessions between the two. That's about as good as you can do without using a third party program.