Inviting: the Companion's welcoming ceremony in Firefly.
Comforting: Mrs. Bridges in Upstairs Downstairs.
Definitive ordering: Picard and his Earl Grey in Star Trek: TNG.
Ethnic caricature: Mickey Rooney in Breakfast at Tiffany's.
Badly timed: Arthur Dent crashing the Heart of Gold's master computer by asking it to synthesize a cuppa in Hitchhiker's Guide To The Galaxy.
Ill-fated: Sen-no-Rikyu's tea-orgy with Hideyoshi in Rikyu.
Your picks?
-DM