E.g. I like archiving applications and on my drive I already have at least three dozen applications which are nowhere to be found on the internet and I just don't know how to preserve this info for posterity.
Well... The first and biggest potential hurdle you'll face is licensing.
If that is not a problem, there's many free web hosts, or you can put stuff on the likes of google's cloud thingy (or dropbox or mega.nz or...) and posts the links somewhere (pastebin? Here? Your favourite farcebork page?)
You could go really weird and rare and set up your own server on a Raspberry Pi with a SD card of suitable size (imaged somewhere else for backup purposes as well).
It's pretty easy these days to get simple hosting done, especially if you're careful to retain your own copies in case (/when) the host disappears or stuffs you around (eg photobucket, google, MS, copy.com, flikr.......).
And there's also the likes of GOG (Good Old Games) - there may be an apps version of them out there?
The only thing that would slow me down (maybe) is the licensing issue. But I'd be hoping to find the original authors and get them on side anyway, though that is often very hard to do.
I used to run a BBS. I had several of the Fidonet 'file echos' feeding into my system. One day I realised I hadn't heard the modem answer a call in weeks so hit the power switch and plugged a phone in. A while later, with no calls coming in, I packed up the drives and got rid of the old case. The drives and SCSI card are sitting in a box in my office desk (yeah, I actually do have an 'office' I visit from time to time) just waiting for me to be board of El Reg/Games enough on a wet day to actually sit down, test and old mobo/psu I have (ISA SCSI card) to make sure it won't blow things up, then plug them all back in and recover the data. Even have an ISA network card, though I may have to hunt back through time to find a protocol I can use to upload the data. Plan is to image the drives and see if I can run stuff in a VM. I have a huge archive of Fido messages I've been meaning to ship off to someone as well, I may even have the biggest surviving collection - IF the drives still run.
So if you do find a place that will take old programs let me know, I may have some they're interested in :)