...Yes, each Mangekyo Sharingan has an ability unique to itself. Also, if I may make note, Sasuke DOES HAVE Tsukuyomi. In order to manifest the Susanoo, you need both Tsukuyomi and Amaterasu. Besides, Sasuke used it on Danzo and at the Kage Summit... it however is very weak compared to Itachi's.
Kakashi has
Kamui (The long-range, black-hole space-time ability).
Shisui had
Kotoamatsukami (A genjutsu so powerful no one can detect that he or she is under a genjustsu. Perfect influence without the opposing party knowing).
Sasuke has
Blaze Release (It allows him to for all intensive purposes, perfectly control Amaterasu. He can use it as a shield/barrier or individually target multiple enemies all at once).
Itachi, although never directly stated, has the ability to see into and take things from the spirit realm, hence why his Susanoo has two of three legendary weapons.
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Tobi... it is debatable if he has the Mangekyo or not, nevertheless, his Sharingan has the ability to absorb and reject objects, people, and himself out of his own dimension.
Madara, and
Izuna have never been seen using unique abilities, as of yet.