Apart from native instruments, such as the balalaika. kantele, hardanger fiddle, pipa, shakuhachi etc, concertos for most orchestral instruments have been written, & in the past 30 years concertos have appeared for the less likely solo instruments.
One surprise is the Contrabassoon. Kahlevi Aho's (b1949) concerto was released recently on BIS(CD 1574).3mvts 34'22". It requires a specially developed instrument capable of reaching over an octave higher than the standard instrument. The concerto is surprisingly lyrical, almost a symphony for Contra & orchestra, and in the highest register sound like a heckelphone or saxophone. Aho uses both of these instruments in the orchestra and the work contains duos & trios for Contra with both istruments.
There are many other Contrabassoon Concertos in the catalogue, including those by G.Schuller (b1925) D.Erb (b.1927), V. Muradian (b1921),E.Schuloff (1894-1942), B.Cummings (b1946),M.Doran (b1921), with a number of 18th/19th century concertos transcibed for the Contra.
Susan Nigro, renowned Contra player, has released a number of discs on the Crystal label.
Like the Trumpet, Trombone & Tuba, the Contrabassoon repertoire would be of interest mostly to bassoon players and those like myself out of curiosity, and is an acquired taste.
The Aho booklet states that the first Contrabassoon concerto was written by Gunther Schuller in 1978, but according to Oscar Thompson's Cyclopedia, Ruth Gipps wrote hers in 1969.
Concertos for Bass Clarinet are much rarer.The only one I have on disc is the concerto by D.Erdmann (b1917), (MDG) although a number have been written in Scandanavia particularly.
Robert Simpson (1921-1997), has written a Quintet for Bass Clarinet, Clarinet & String Trio. (1983).
I do not know of any Hecklephone concertos, and they are rarely used in the orchestra. (which is a pity, as the instrument has a beautiful mellow sound). Paul Hindemith's Trio for Hecklephone, Viola & Piano (Chandos 9990), demonstrates its qualities very well.
A Xylophone concerto has been written by T.Mayuzumi (1929-1997) (ASV CD DCA 1126), and the only other I know of, was written by K.Pringsheim (1883-1972).
Few concertos have been written for Cor Anglais. Donizetti's is probably best known, but other composers include Wolf-Ferrari,Honneger,Rorem,Vasks & Gordon Jacob (rhapsody)
An unusual concerto worth mentioning, is the Triple Concerto by Don Martino (1931-2005),(Albany Troy 168), for Clarinet, Bass Clarinet & Contrabass Clarinet, where the composer treats the three instruments as a single instrument. It is in 3 mvts (25'54"), and after repreated hearings, I have grown to like it.
Naxos recently released a disc of Euphonium Concertos.(8.570725)
The extensive use of the Triangle in Rott's Symphony,(particularly the BIS recording), while not a concerto, keeps the Triangle player busy. Later recordings have reduced the triangle part. Liszt used the Triangle extensively in his 1st Piano concerto (3rd mvt), but the extended use by Rott is unprecedented.
There must be many more to add to this list ?
Marcus.