One of the things that started to annoy me when using FireFox was that it seemed to only allow meI to do 6 downloads from a site at a time. I would click on 6 downloads and they would all start, but when I click the 7th link, it would sit there until one of the previous downloads completed.
So after some digging I found that this is actually quite simple.
1. In the address bar type about:config. This will list all the possible configuration options with FireFox. Be Careful!
2. In the filter type http.max
3. Double click on the network.http.max-persistent-connections-per-server. This will display the Enter Integer Value dialog box.
4. Set the value to whatever new value you want.
5. Press OK to set the value
FireFox does not need to be restarted for this value to be set.
I would not set this number too high as it could slow down the overall speed of the download. I set it to 10 as there were 10 files I needed to download and I did not want to wait for one to finish before I started the next. I just wanted to click and walk away and come back in an hour :)