Many cinema chains in the UK have offers like this. My girlfriend has a cinema card that costs her £15 a month and allows her to see any film she likes (although she has to pay about £1.50 extra to see 3D films). This is an offer that's been available for at least 8 or 9 years. Tickets for 2D films in the UK typically cost around £7.50 (higher in London).

Granted this cinema card is only useable in cinemas belonging to the same chain.

Do any US cinema chains offer similar services?