The poor twelve-sided die doesn't see much action in most D&D games. It's in an awkward in-between range, where gamers tend to prefer bell curves over equal probabilities. The d12 ends up losing the popularity contest to 2d6.
I'm pretty sure...well, quite sure, actually, that somebody somewhere has already had this idea. It's one of those things that's so obvious once it's there in my head that I can't imagine that it hasn't been thought of before, but I can't recall ever seeing it, so I'll throw it out there now.
The d12 is just about ideal for randomly determining time of day. Roll any die you like to determine a.m. or p.m. (even or odd) and then give the old d12 a roll to find the hour.
By the same token, if you need to determine a direction, the d12 rises to the task, using the clock face analogues for relative directions. Someone got disarmed and you want to know where his dagger went? Roll a d12. 12 is straight in front, 6 is directly behind, with all points in between covered. An encounter in the wilderness that could be approaching from any direction? Roll a d12. Dragon coming in fast at 3 o'clock!
Not so useless after all.