The Second Doctor owned a recorder which he enjoyed playing, mostly as a source of self-amusement, but also to help him think. While his future incarnations often relied on the sonic screwdriver as their favourite tool, this Doctor preferred the recorder as an all-purpose utenstil.
He played it several times while on Vulcan, (TV: The Power of the Daleks) in a marketplace on the Panjistri homeworld to amuse Lilith, (PROSE: Timewyrm: Apocalypse) while in a Scottish prison cell, (TV: The Highlanders) while visiting Atlantis, (TV: The Underwater Menace) while visiting an Earth colony, (TV: The Macra Terror) while imprisoned by the Daleks, (TV: The Evil of the Daleks) while imprisoned in Tibet, (TV: The Abominable Snowmen) and while under Robot Yeti guard. (TV: The Web of Fear)
When the Doctor's TARDIS landed in Australia, Jamie made the Doctor leave his recorder in the ship before they went out. (TV: The Enemy of the World)
Jamie once chopped up the recorder, but it didn't prevent the Doctor from producing a new one from somewhere. (PROSE: Twin Piques)
After escaping from the Land of Fiction, the Doctor realised he had left his recorder there, and sent himself back in to retrieve it. While there, he encountered Goth, who asked him to help the Time Lords, and thus sent him to meet his future self. (PROSE: Future Imperfect)
When the Second Doctor and the Third Doctor were transported to Omega's anti-matter universe, the recorder fell into the TARDIS' force field generator, and was therefore not converted into anti-matter during the trip. When the Doctors discovered this, they offered it to Omega, and the resulting annihilation seemingly destroyed the renegade Time Lord and his world. In exchange for his sacrifice of the instrument, the Third Doctor promised his earlier self that he would buy him a "thousand" more. (TV: The Three Doctors)
Although his memories of meeting his future self quickly faded, the Doctor did remember that he had lost his recorder, and went to a music shop on Amber Station to get a new one. (PROSE: Briefly Noted)
Once, the Doctor combined his recorder with his sonic screwdriver to communicate with a Doredsor. This enabled him to translate colour to binary to Solresol to musical notation and back again. (PROSE: The Time Eater)
He gave his recorder to Flora Millrace, claiming to have extras. (PROSE: The Avant Guardian)
On Trodos, the Doctor used his recorder on a Dalek's hearing system, sending it out of control. (COMIC: The Trodos Ambush) On a swamp planet, he used it to stop giant spiders from attacking him and his companions. (COMIC: Master of Spiders) On prehistoric Earth, he used it to befriend a herd of mammoths and get them to destroy the Trods' power supply. (COMIC: Pursued by the Trods)
Other references
Sarah Jane Smith discovered the Doctor's recorder in the TARDIS' secondary control room. (TV: The Masque of Mandragora)
The newly regenerated Fifth Doctor tried playing the recorder, but realised that it was not for him. (TV: Castrovalva)
The Sixth Doctor, confused by a time-slip with the affected Second Doctor, tried to remember a musical instrument important to him. He mentioned a clarinet and a flute, before recalling it was a recorder. (TV: The Two Doctors)
The Eleventh Doctor left a recorder in his TARDIS drawing room. (GAME: TARDIS)
Modifications
The Doctor often added modifications to his recorder, allowing him to put it to unusual tasks. The Doctor used his recorder as a spyglass on the Silver Carrier. (TV: The Wheel in Space) He repeated this trick in Tobias Vaughn's base. (TV: The Invasion)
In Atlantis the Doctor used his recorder as a blowpipe, expelling powder into Zaroff's face. (TV: The Underwater Menace)