Decimal Time
Many and various attempts to base time on base-10 like the rest of the metric system. There are more systems than I care to recount here, but John Hynes Decimal Time Site has pretty complete list. Some notable systems:
Image: Wikipedia
10-Hour Systems
Probably the most notable system is French Revolutionary Time. A day has ten hours, each with 100 mintues, each with 100 seconds. Another version is the Metric Clock Widget.
Decimal fraction
Instead of hours, there is simply the decimal fraction of a day, usually reported to 3 decimal places. Typically the system is based on a UTC like coordination, where the time is the same everywhere, and residents of each area need to know their local midnight. Days are often counted as simple linear count. An example is the Decimal Time Project, with date-times like 077.830D752.872. There is DTP Dashboard Widget.
Image: Watch Report
Swatch Internet Time.
A variation of Decimal Fraction systems, using @ and exactly three digits, called beats. Example: @123. The origin of the system is the Company's headquarters in Biel, Switzerland. It makes no modification to the counting of days. There is an iBeatTime Widget.
Digital Time, and Other
Image: Wikipedia
Hexadecimal Time
Divides the day into 16 hours (0-9 and A-F) instead of 24. This is slightly closer to the current system then decimal time. Hours are broken down in to 256 (00-FF) minutes; minutes are broken down into either 16 or 256 seconds depending on the system. Wikipedia has a brief brief but sufficient introduction to hexadecimal time
An interesting feature is that the hours are 90 minutes in the 24/60 system, which is claimed to be a natural period for human activities, especially sleep. The Child Sleep Cycle Calculator is based on a similar theory of 45 minutes.
Disk Clock has a unix time disk
Unix Time
Simple serial count of seconds since 1970-01-01. There are various versions with different time bases. The Decimal Time site has a page on various computer times.
New Earth Time
A global time like DTP and Swatch internet time, but measured in degrees, minutes, and seconds. An example might be 179° 31"
28-hour Day
Proposes switching from 24/7 to 28/6 to reduce 'overhead' events like travel.
Unusual Clocks
Strange ways of representing time, often using the traditional 24/60/60
Color Clocks
Polar Clock is a flash program that shows various time periods as color arcs. The polar clock is very much in the spirit Disk Clock - revolutionizing time. When I first found I thought I might be able to save myself the trouble. But it doesn't do it for me personally - I prefer the bigger periods on the outside (I rarely care about the progress of second) and my reading position localized.
Colhour Clock is an interesting variation on the color-as-value theme - it's all about color. I find it kind of hard to read - using color like this for one disk might work well, but using it for all of them washes out the distinctions between each.
There are several variations; this one at least gets the seconds on the inside, and the smaller number of disks is easier to sort out. (I ended up coming to a similar conclusion with Disk Clock)
The Chromo people actually claim that color is directly associated with time due to daily and seasonal daylight cycles. They have a Chromo Dashboard Widget
Last Clock
Uses a ring arrangement like Disk Clock, but moves the hands. The main novelty is that each hand is drawn using a live video feed. I might prefer a 24 hour version, but the day/night difference on the hour hand is quite distinct.
Ambient Clock
The data junkies at Ambient Devices wrapped twelve hours of Google Calendar around a clock face. Especially novel is displaying the travel time based on a Google Maps estimate of the travel distance.
Mechanized Sundials
The Bulbdial Clock rotates lights around a central pole, to create shadow hands. The comments on this lead me to...
The Annosphere is a sort of artificial-sun dial which moves the dial rather than the light (which, really, is a more accurate simulation.) it also has a year disk to track the constellations and months.
Image: Wikipedia
Marshalite Traffic Signal
Not precisely a clock, but it uses a disk representation to better inform travelers. As the article notes, however, it cannot change speed to respond to actual traffic.
Realities:united Massive Digital Ceiling Clock
Room lighting by a pair of 7-segment displays, showing the minutes part.
Found via Information Aesthetics, whose entry on the ceiling clock includes the time-lapse video.
VelaClock
Covers some of the same ground as Disk Clock, more completely but also in a more piecemeal fashion; each type of information has it's own display. They do include a daylight display, which I obviously approve of.
Disk Clock also shows daylight, although I picked one arbitrary period of twilight rather than trying to draw all three official ones.
Fractal Clock
A Laudable attempt to revolutionize time. Unfortunately I find it hard to read because of the different directions; a lack of indicator markers doesn't help. The intro mode is quite nice, however, given the strangeness of the concept.
Binary Clocks.
Many and various implementations, showing the standard 12/60 digits (and sometimes others) in binary. An example Binary-Coded Digital Calendar/Clock.
Set Theory Clock
Based on representing time with the fewest number of on/off indicators. I rather like it, though sometimes I want sub-minute precision. Of note, this one has a physical incarnation in Germany.
There is a Set Theory Clock Widget. A variant is the Decimal Clock Widget
Analog Bargraph Clock
A few conceptual similarities to Disk Clock - one indicator per unit - but not nearly as pretty.
Timeline
Another one that made me reconsider the necessity of Disk Clock. But the single color is kind of boring, and the flying seconds are kind of distracting.
Calendars
Living Calendar
A calendar constructed like a standard dial-and-hands clock, with two scales for days of the year and week. The year dial includes the things you'd expect from a calendar - holidays and other events.
Disk Clock shows the Tzolk'in, and I think it's a rather nice way to view the interlocking cycles.
Tzolk'in
The mesoamerican cultures had a fascinating calendar system based on interlocking cycles of 13 and 20. (Tzolk'in to the Maya, Tonalpohualli to the Astec, and probably other names to other cultures.) Unfortunately, this only accounts for 260 days, so it was usually combined with a solar year counting system based on similar principles, but using a more traditional month/day arrangement. (The Haab) The combination of dates between the two systems repeated every 52 years, which became a time of major celebration.
Disk Clock has disk sets for both the apocalyptic 13-baktun, and the 20-backtun.
Long Count
The long count is another mesoamerican calendar. It was used for recording large scale events that extended beyond the 52-year cycle. It was based on 'digits' of 20, with one 18 to make the lower two digits approximate a year. There are at least two versions - one popular rendition has a digit of 13 instead of 20, which will cause the whole cycle to roll over at December 20, 2012. (The other view assumes that the digit counts to 20, like all the rest.)
Death Clock
Countdown of seconds until your death, based on a few health-related questions
If you're up to editing the html file, Disk Clock can show the time until you turn 80, but the time of death isn't yet customizable.