DubConqueror: Might and Magic VI has an in-game calendar that has effect on when you can travel: ships only leave port on certain days of the week. Plus there's a carnival takes place in a specific month and maybe there's more calendar-bound events (I only played the beginning of the game).
This reminds me:
Might and Magic 2 has a calendar, which affects two things, to my knowledge:
* There's a spell called Nature's Gate which takes you to different places depending on the date. Later dates in the year tend to take you to more advanced locations.
* There is a circus that only appears at certain dates.
Darvond: Avernum had an internal calendar that would occasionally come up in the form of "Here's a discount" or just a note in your message log.
To my understanding, Avernum 3 took it even further; if you took too long to do certain things, cities would fall into worse shape as time went on. Furtheremore, there is an event around day 180 (IIRC from what I've read) that, if not solved in time, will result in a game over.
(How does Avernum 3: Ruined World handle this?)