Imagine putting a git-annex drive in a time capsule. In 20, or 50, or 100 years, you'd like its contents to be as accessible as possible to whoever digs it up.
This is a hard problem. git-annex cannot completely solve it, but it does its best to not contribute to the problem. Here are some aspects of the problem:
How are files accessed? Git-annex carefully adds minimal complexity to access files in a repository. Nothing needs to be done to extract files from the repository; they are there on disk in the usual way, with just some symlinks pointing at the annexed file contents. Neither git-annex nor git is needed to get at the file contents.
(Also, git-annex provides an "uninit" command that moves everything out of the annex, if you should ever want to stop using it.)
What file formats are used? Will they still be readable? To deal with this, it's best to stick to plain text files, and the most common image, sound, etc formats. Consider storing the same content in multiple formats.
What filesystem is used on the drive? Will that filesystem still be available? Whatever you choose to use, git-annex can put files on it. Even if you choose (ugh) FAT.
What is the hardware interface of the drive? Will hardware still exist to talk to it?
What if some of the data is damaged? git-annex facilitates storing a configurable number of copies of the file contents. The metadata about your files is stored in git, and so every clone of the repository means another copy of that is stored. Also, git-annex uses filenames for the data that encode everything needed to match it back to the metadata. So if a filesystem is badly corrupted and all your annexed files end up in
lost+found, they can easily be lifted back out into another clone of the repository. Even if the filenames are lost, it's possible to recover data from lost+found.
What about upgrades to the git-annex repisitory format? git-annex supports upgrades from all previous repository versions, and will always support upgrading from all of them to any new versions. Note that the upgrade process needs to modify the content of the repository -- if modifying the original archived repository is not desirable you can always make a copy of the repository and upgrade the copy.
What about encrypted special remotes? A(gpg and openssl) can decrypt files stored on such a remote, as long as you have access to the encryption keys (which are stored in the git-annex branch of the repository, sometimes encrypted with your gpg key).