Blues was a genre of music. The word was also used to describe a feeling of depression.
Two subgenres of blues music were Andorian blues and skuzz blues. (TNG: "Unification II"; LD: "In the Cradle of Vexilon")
In 2152, Charles Tucker III played the blues on his harmonica in his quarters. (ENT: "Precious Cargo")
In 2259 of the alternate reality, having received word that he was going to be sent back to Starfleet Academy following an incident involving the violation of the Prime Directive on Nibiru, James T. Kirk visited a bar in San Francisco where blues music was played over the speakers. (Star Trek Into Darkness)
In 2368, Commander William Riker asked Amarie if she would play some blues music on her piano. She claimed to know seven shades of blues, then asked him if Andorian blues was a good choice, and began playing it for him. (TNG: "Unification II")
In 2381, Commander Jack Ransom told Ensign Beckett Mariner that she should be there for Brad Boimler since he was experiencing grief. He went on to tell her that "when I've got a case of the blues, I lean on my besties pretty hard. I don't know what I'd do without Honus the bartender, Nurse Westlake and Matt the whale." (LD: "Crisis Point 2: Paradoxus")
In 2384, while in the holodeck, Murf was lip syncing the song Smile and Forget It. One of the lyrics of the song said: "With your cup half full I swear those blues won’t stay." (PRO: "Ghost in the Machine")
In 2399, Cristóbal Rios was listening to blues and drinking alcohol when his ENH interrupted, telling him how excited he should be that Jean-Luc Picard would soon be on his ship. Rios, annoyed, deactivated him. (PIC: "The End is the Beginning")
Blues was described by the Star Trek Encyclopedia, 4th ed., vol. 1, p. 327 as an American folk music. One of the musical instruments associated with this genre was the harmonica.