See: Aria2, I've had a bit of time with it and think it's pretty neat. Couldn't get it to torrent well, but that's more likely my internet.
wget? Doesn't support several connections, but it's a brilliant downloader regardless, and has windows and linux ports.
Opening multiple connections isn't as great as it sounds, anyway. If the server you're downloading from doesn't cap the speeds it's useless, and if it does it probably does so for a reason - meaning you're likely to annoy the administrator, possibly to the lengths of an IP ban (which would limit your connection speeds a lot more than only having one connection ;))
Aria2 looks to support it, but I've always been happy with wget.