Ask HN: Is it worth paying $200 to get 16gb RAM on mid-range Mac mini?
If you are buying a 2014 model, given that it seems to be non-upgradeable, I suppose the answer is "yes if you want that much memory." Whether you want that much memory depends strongly on your application needs.
If you already have a 2012 mini or earlier, I would look at crucial.com. It looks like the 2012 models are pretty easy to upgrade. Older models, I know from personal experience, are quite fiddly and difficult to take apart, so I wouldn't recommend it unless you have experience taking apart laptops and tools available such as spudgers and spatulas and extra kapton tape.
FWIW, i used a mid-2011 2.3Ghz i5 with 8 GB of RAM for about 4 years as a lightly used dev machine (read: basically ruby/rails, pg, and sublime text with some crud stripped out and running on OS X [not server]) that also hosted about 25-30 (low bandwidth) rails apps for internal use that did a lot of text processing and never really had too many complaints. flash forward 2 years of sitting idling without any activity and it's a bit sluggish now (granted that's because i've done literally nothing on the machine other than let it run)
What is it being used for?
Mostly for development purposes, running an IDE (Eclipse or IntelliJ), Android emulator and a local Apache server. Besides development, I might have light usage of Photoshop but no video editing or gaming.