How often do you actually refer to a specific date (October 1st, third day of the first moon of spring, etc.) or year in your campaign, rather than a relative date? (Next week, two days from now, next summer?)
I've used the relative time a lot but it occurs to me that even when I know the former, it doesn't actually come up in play much. In Risus Monkey's Buffy game I usually knew the exact date, but that was because it
was a real historical date, (the game was set in the early 90s) and
since we were college students, what holidays were coming up and whether
it was the weekend or not was pretty important. Also, because we used
the actual weather in the area from that date, part of the "beginning of
session" ritual involved looking up and discussing the date.
In Trollsmyth's game I have no idea what the calendar date is and never have. This is
partly because the pace of that game tends to be really slow, but also
because, as adventurers, what I care about in terms of time is "how long
until we get to the dungeon?" and "how does it take to recover from the
last dungeon?" It also just doesn't come up a lot from other
players/characters in the game. If Brian mentioned it at the start of
every session I'd probably remember.
I seem to remember doing
that in the cyberpunk/post-apocalyptic d20 Modern game I ran in high
school, and I think the people who cared remembered and wrote it down. I don't know that we used it that much, in play or in talking about play, though. Same with the Arcana Evolved game I ran at the end of high school. I don't know that I've even known myself in all the games I've run since then, although that's partly because they've been rather scatter-shot. I haven't started keeping real thorough track of time in the ACKS game, but I've been keeping the notes that I'll need to go back and normalize it if/when I decided specific dates are important.