There is a [relatively] well-known version of the Sibelius concerto with piano accompaniment (authentic transcription by the composer); it's often used by students in Finland and has even been recorded.

The original version of the concerto also had a piano transcription - or at least most of it did. Now the missing sections (I believe mostly in the first movement) have been filled in by Kalevi Aho, and it has been performed in this form in Tokyo, by Madoka Sato and Folke Gräsbeck.

Watch this space for updates!

I remember first hearing the "official" transcription of the final version (live) at the grand opening of a bookstore in Ostrava, CZ. I could swear I could "hear" the orchestra...

It was in "From Mao to Mozart" - the Isaac Stern film... it sounded interesting, but there were only the first few bars of the piece in there. I'd like to hear it, actually, though I would think that it would sound a bit more "clunky" than with orchestra. After all, the piano was never built for the seamless opening in the violins.