Looking for files NOT owned by a specific user

The find(1) utility has primaries that can be negated ("reversed") using the "!" operator. On the prompt one must however escape the negation with a backslash as it is a shell metacharacter. Result:

find . \! -user foo -print

Looking for files NOT owned by someone

Others have answered the question "NOT owned by a particular user" in the body. Here's one that answers the titular question but has not been provided:

$ find / -nouser

You can use it like so:

$ sudo find /var/www -nouser -exec chown root:apache {} \;

And a related one:

$ find / -nogroup

-user finds by user or user ID, and ! inverts the predicate. So, ! -user ....

You can use this:

find <dir> ! -user <username>