Utopian Clocks (Proposed)
Fully Binary Time
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This clock is based on a proposal from Dripfeed and envisages the day as a seventeen-place binary tree. The day is first divided into two twelve hour period, which are each subdivided into two six hour periods, then two three hour blocks and so on; the smallest integral unit of time is about two-thirds of a second. Source code is available, should you wish to install this clock on your own computer. Alternatively, a crudely constructed Dashboard widget is available for users of Mac OS X 10.4 and above.
French Revolutionary Metric Time
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During the French republic of 1793 - 1795, metric time was the official horological system. Under this system, there were ten hours in a day, a hundred minutes in an hour and a hundred seconds in a minute. A similar calendar was used, although the unpopularity of longer working weeks contributed to the fall of the republic.
The 28 Hour Day
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It has been suggested, that it is possible to abolish Monday! A week's 168 hours can be divided perfectly into six, twenty-eight hour days instead of the usual seven. And you would never wake up wondering which day of the week it was, as they'd all have idiosyncratic differences in relation to the outside world. And you wouldn't have to go to work as often, either!
Hexadecimal Clock
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Tricky suggested this clock, as ten is apparently a silly number to count in, and as sixteen is a power of two, it'd make the job easier for computers. It would also make the compass points and directions in "o'clock" form correspond, it seems. Under this horological regime, there are sixteen hours in a day, made up of 256 minutes of 256 seconds each.
Angular Clock and New Earth Time
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Another clock proposed by Tricky, one that measures time in terms of the Earth's rotation around its axis. Time is represented by the angle between your time zone and the one where it is currently midnight: how far round you've gone today. If we did away with time zones and all measured time by the Prime Meridian, then we'd have New Earth Time, which also used rotation to measure the day.
Chrons and Swatch Beats
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This is another flavour of metric clock, dividing the day into a thousand units called chrons, thought up by Seth Golub in 1994. It's rather similar to Swatch's Internet Time scheme propounded in 1998, though it recognises that time zones are actually quite useful for most of us. Conveniently, a centichron is roughly a second long, aiding any luddites out there, whilst Swatch's well-known scheme doesn't provide for any subunits, making the shortest unit of time 86.4 seconds long. Swatch took a ride on the nepotism bus when cooking up their scheme, as all time is based on mean time at their Swiss headquarters, rather than the universally accepted Prime Meridian.