I'd like to clarify a few things said so far in this thread:
1) Provider limitations for direct download aren't tied to the number of connections you're making. Certainly, there are some direct download sites which may limit you to say 200k/s per connection and allow download managers, but this has no affect on what their provider limits their connection to. For each server they rent, they pay for a specific bandwidth switch port, and that's what they get (assuming their provider isn't overselling). Typically this is 10 or 100Mbps, although it could be Gigabit or 10GigE for that matter.
2) Because torrents use a swarming affect, it's possible to saturate your bandwidth if its well seeded, regardless of the individual status of the seeds, unlike in a direct download scenario where the status of the download site makes all the difference. During peak hours on a download site, you may encounter contention, even if they haven't saturated their provider bandwidth limit, but during peak times on a torrent, it just gets faster (unless it's during initial seeding).
3) Upstream and Downstream are separate. In a symmetrical connection, like most business-class leased lines, these speeds will be the same. In most residential connections, these speeds are different, thus making the connection asymmetric. There are some specific limited times where downstream and upstream can cause an interaction, but these only occur during peak hours on shared node type connections such as cable Internet in a residential scenario, and only if the node is oversold.
Most providers make an effort to not heavily oversell their nodes, so typically even in these shared scenarios you won't see this effect, and certainly as cable providers make the move to DOCSIS 3.0 to provide IPv6 support, you'll see nodes upgraded to the point this will no longer be the case.
Typically these issues come about because the node itself is limited in bandwidth and has to schedule the usage of each household connected to the node so that the total usage of all households served from the node doesn't exceed the total bandwidth capacity of the node. In order to gain DOCSIS 3.0 compliance, cable providers must run fiber-optic links to their nodes which can have the bandwidth scale dynamically based on the equipment being used on either end (i.e. they don't need to run a new line, as they did before with copper). Typically you see fairly high bandwidth links being run to the nodes. In a more typical scenario where the residential connection is being provided through some form of DSL, or something like FiOS, the downstream and upstream links do not have any way to affect each other. This also has absolutely nothing to do with TCP.
4) This isn't to say you don't have other factors to worry about. When you're downloading via a direct link through a service like HTTP or Usenet, you may be unable to saturate your connection, but you also don't have to worry about causing contention on your edge device, because the number of connections and the connection overhead is relatively low. In the case of swarming protocols like Bittorrent, instead you often see routers collapsing under the connection load, which can cause performance issues for other users or services on the network even if there is plenty of bandwidth left to go around.
Additionally, a portion of the bandwidth being used which "saturates" the connection in a scenario where that's happening is being used for protocol overhead and not for data transmission. Typically this is a relatively small amount, however as you increase the number of connections required to saturate the link, you're also increasing the overhead. Depending on the link speed of each of your seeds, there are situations in protocols like Bittorrent where less connections can actually be better than more connections for actual data speed (i.e. you have a 10Mbps downstream, with 5 seeds you're using 8Mbps downstream, but transmitting 7.8Mbps of data, with 10 seeds you may be using 9Mbps of downstream but transmitting 7.6Mbps of data, although this is example is not in line with the actual growth of overhead for the protocol, it's useful to illustrate the point).
5) This conversation is like watching a monkey fuck a football. Everybody should go and read this book. It's hardly what I'd consider to be the best, but it provides a good overview nonetheless. You're all making me sad for the future of humanity, so stop it.