In theory, no — that's essentially the entire point.
In practice this is much more difficult, but simply storing static, encrypted files on a remote machine is actually one of the less error-prone uses of cryptography. There are comparatively fewer avenues of attack than, say, encrypted session protocols or cryptosystems that manage and federate access to multiple users.
Of course, there are ways to complicate this; for instance, Tarsnap stores encrypted backups on a remote server, but uses novel cryptographic tricks to do so while performing aggressive deduplication. Once you start adding complexity like this, the possibilities of a privacy-destroying mistake increase. But if you're using something like GPG with reasonable key lengths, outside of any major breakthroughs in cryptanalysis, you can reasonably expect your data to remain private.