First before actually archiving data there is one very important question to ask yourself:
Do I actually care?
10 000 images is a fairly large collection. I've seen far larger collections of Data in my time, and I'm sure lots of photographers hang on to far greater collections than that, but why are you storing all of it?
Are they All important? Do you see yourself wanting the entire collection again at a later point in time? Is it impossible to cull this down to a more reasonable number?
After you figure out what you really need to store, then start looking at your options.
Personally I'm kind of a fan of Network Attached Storage (NAS) boxes, because of how easy some models are to use and setup. And they can be stashed in out of the way places, rather than taking up extra room right on your desk or near your computer.
For files that are really important, then you really want to use off-site backups. That way if something happens to your home, you don't lose your stuff. Well, all of your stuff. Currently I have a cross-share setup with some friends, which is basically a custom script we have setup using the program Unison to sync folders at each other's houses. We each get 1/4 of a 1.5TB drive, and every week that drive gets archived locally at each location. (The archive is to prevent someone from doing something foolish, like accidentally deleting files from their folder, and then passing that change around to all the others. In theory we can't lose more than a week of work.)
Failing tech savy friends to do something like that, then I would consider one of the many "Cloud" based services for online backup, combined with a nice little encryption system on your files before you upload. Just remember the password to your files. DropBox lets you backup 2GB of your most precious data for free.
However, I would not suggest relying on any free service as your critical archive method, or even a single service if your work is exceptionally critical.
Canon EOS 7D | EF 28 f/1.8 | EF 85 f/1.8 | EF 70-200 f/4L | EF-S 17-55 | Sigma 150-500