Certainly not on the web, it’s disallowed in the HTML5 spec:

User agents must not support the CESU-8, UTF-7, BOCU-1 and SCSU encodings.

and major browsers removed support, e.g.:

https://bugzilla.mozilla.org/show_bug.cgi?id=414064

Not sure if this "counts," but it is still used to encode IMAP folder names. (Technically, the IMAP version is slightly different from standard UTF-7.)

I'm confused by that as well. I never really understood the motivation behind it - though I guess it's obsolescent, so hopefully it'll soon be just another one of those amusing anachronisms we see occasionally in computer science.

As I understand it, the motivation was to be able to transmit Unicode text over a channel that's only 7-bit safe (e.g. mail protocols) without having to do something silly like Base64-encoding the whole thing.