Number one is a title affectionately given to an officer who is second in command, literally because the first officer is, in name, the commanding officer's "number one" man (or woman).Christopher Pike referred to his first officer as Number One. (TOS: "The Cage")
Captain Picard also referred to his first officer, Commander Riker, as number one. (TNG: "Encounter at Farpoint", et seq.)
After his assimilation by the Borg, Picard (as Locutus) also chillingly referred to Riker as number one. (TNG: "The Best of Both Worlds, Part II")
Doctor Beverly Crusher also once referred to Commander Riker as number one. (TNG: "The Battle")
In Peak Performance, when the crew prepared to effect their ruse against the Ferengi, Picard said "Are you ready, Number One?" and both Riker (on the Hathaway) and Data (as acting first officer) answered him.
In Peter David's novel Vendetta, Captain Morgan Korsmo, captain of the USS Chekov referred to his first officer, Commander Shelby, as Number One.