I can open a terminal and wget it, or paste it into a web browser, but is there a way to do this from within unity?
But you can try steadyflow download manger it will detect link from clipboard
I think, FlareGet would be an ideal choice for you as
But the free version in Ubuntu software center does not support "Browser integration", you need to pay $10 to get browser integration plugin. I guess without browser integration, download manager won't make sense.
So here is the workaround to get Browser integration for Firefox. I have tested it on Firefox 18 and it works like a charm.
Just right click any downloadable link and choose FlareGet.
I love Firefox so this is enough for me. Something similar can be worked out for Chrome.
Then write a bash file getlink.sh (I put mine on the desktop)
allow it to be an executable.
Create a launcher on your desktop and edit it with gedit so that it looks something like this:
If your link was the last thing you copied this should download the file and paste it on the desktop.