A cape was an outer garment that was attached at the neck or over the shoulder and would have various lengths down the back. Some capes would have hoods while others did not. A cape was commonly used to protect the wearer from the weather and could be made out of various types of cloth.
While Spock and Lieutenant Dawson were disguised on Kyros they wore various colored capes. When Kirk prepared to beam down to the planet, he wore the cape of a Kyrosian sea captain. Ensign Sarah George wore a long black cape. (TOS novel: Spock, Messiah!)
Hikaru Sulu wore a black cape while performing a magic act with Nyota Uhura and Pavel Chekov on the USS Enterprise. (TOS comic: "So Near the Touch")
Michael and Patricia Bickley wore capes as part of their Starfleet uniforms. (TNG comic: "... Where No One Has Gone Before!")