If this question is too vague, I'll gladly accept criticism to narrow the focus. I'll throw in some specific queries to get a jump start - I'm not interested specifically in the history of mechanical clocks (though I like that history too), but "time" as a more general concept.
What kinds of natural phenomena have been used as "clocks"? I'm familiar with the nail-in-candlewax, sun dials, mechanical clocks - are there lesser known "clocks" that have been used? Who used them, and for what purpose? Were there any cultures who had unique needs or desires that led to different timekeeping methods?
Have units of time always been understood as objective and the same for everybody, everywhere? For example, barring relativity/minute measurement issues, I believe that one day is roughly the same duration as another and can be subdivided into equal parts. In the past, was there ever a perception that over long distances time could be somehow "different"? Maybe like Lothlorien in Lord of the Rings?
I'm curious about anything to do with time and clocks!
One interesting cultural practice that resulted in careful timekeeping was Greek oration. The practice of trials and public speaking lead to the use of the water clock in order to ensure opposing sides had the same amount of time to speak. A clepsydra is essentially a large pottery vessel with a small hole in the bottom. Then, it can be filled to various points, and it will empty itself in a predictable amount of time. This can be used to ensure even units of time over and over again.
The water clock, or clepsydra, is believed to have been invented by the Egyptians, but they didn't make as much use of it as the Greeks, so it is culturally more associated with the Greeks!
Other cultures that had unique timekeeping needs were classical Islam, where astrolabes were used to determine the exact time of the multiple prayer times through the day and night. The astrolabe was also used to determine the correct direction for prayers.
When you get to timekeeping, one of the most interesting stories I've heard recently is the race to solve the latitude problem. Scientists and navigators realized that if you could keep extremely accurate time aboard a ship, it would be very easy to calculate local time and compare it to the origin time to calculate latitude, but the development of an accurate enough timepiece was long and arduous!