The answer (from my side) is: far more primitively.
I do not have an always-on machine, sitting and downloading stuff. Instead things are downloaded manually to my MacPro. Oliver's use of Dropbox is a master-stroke and one I might just try and copy. It would be the first really practical use for this (pretty neat) service.
On the MacPro I'm running Connect360, which published all movies to XBox, which is directly connected (by ethernet cable, since the XBox doesn't do wireless-N) to an Airport Extreme basestation. The MacPro connects wirelessly to another Airport Extreme, which is bridged to the first one.
The convenience of sitting on the couch with a wireless controller and being able to turn on XBox with it remotely, browse for a movie and play it on my flat screen TV is amazing.
I am running into issues though. Firstly the XBox is noisy as hell. That's fine when watching a Prison Break marathon, but not so much when watching a latest drama or near-silent movie like No Country for Old Men. Furthermore, having a full-HD TV means you really want to watch HD content, yet this is harder than it seems. Most HD content is encoded using MKV, which the XBox doesn't play. Converting that into h.264 is not straightforward and very time-consuming. You need to demux audio and video, encode each one and then recombine them. If the file is larger than 4Gb is needs to be split first, etc.
Even after jumping through all these hoops the result is often a h.264 that stutters like crazy (not a function of the network).
If Apple upgrades the hardware of the mini, I might buy one. Right now mini's aren't powerful enough to play MKV directly either.
The solution I'm eying at the moment is Popcorn Hour. This includes torrent downloading and playing of MKVs. It should also be a lot more quiet than the XBox.
Now if it could only be made to watch a Dropbox folder...