With news of Soundcloud's *possible* incoming demise the general recommendation is to download copies of your Soundcloud hosted material as soon as possible. This of course is based around a worst-case scenario when there's just an 'off-switch' moment for the site, which feels unlikely but could happen.
Soundcloud's UI can feel pretty clunky at times and there's no way to just download all your tracks - apparently this is due to copyright issues (though I'm not too sure why you can't just download all the content you've uploaded).
This CNET article gives some information on how to go through each track and download them individually, but there is a *slightly* quicker way - it still isn't ideal but it's a touch quicker then what was recommended here:
1. (Optional) Change all track privacy settings to "Private"
2. "Enable Downloads" on all tracks from the "Your Tracks" area
3. Download each track individually from the "Your Tracks" area
4. (Optional) Change relevant track privacy settings back to "Public"
Small note - this is going to involve setting all your tracks to downloadable for a short space of time, so if this is an issue then see below to details on how to set all your tracks to Private while you're backing up the files.
In the 'Your Tracks' area you can select 20 tracks at a time; what's very cool is that you can actually select 20 tracks, then move to the next page and add the next 20 tracks to the selection (repeat until you've selected all your tracks). Now you can select "Edit [all] tracks" to manage all their permissions simultaneously. From here you can "Enable Downloads". When this is enabled you'll be able to download the tracks from the "Your Tracks" screen by going through each track individually and selecting the "..." icon, where "Download" will now be an option. Selecting this option will download the track, and you can go onto the next one.
If you'd rather not have all your tracks downloadable for a short space of time, you can also edit the permissions to be Private - select the tracks and go to "Edit [all] tracks>Privacy and Tags" and set them to "All Private". When you're done downloading you can reset the necessary tracks back to "All Public".
Hope that helps - the system is far from perfect, and some sort of one-click backup system would be greatly appreciated; in the short term though this seems like a quick(er) way of keeping copies of material that could (though hopefully won't) disappear in the near future.