Desktop clocks powered solely on water (or any electrolytic fluid such as soda, coffee or even beer) are now available in several designs. The water clock displays the time and date in clear, easy to read numbers just moments after the liquid reservoirs are filled.
It works this this way: The internal converter simply extracts electrons from water (or other liquid) molecules and provides a steady stream of electrical current acting as a fuel cell to generate power to the clock. The clock below can also be used as a vase.

Source Think Geek
In a water powered clock, water is actually used as the conducting agent that completes the electrical circuit for the clock. According to Wikipedia, a slowly dissolving piece of zinc is used as the source of energy that powers the clock. Usage life will vary depending on the amount of Zinc, which could be from months to several years.
The Leeds Element Water Powered Clock needs to have its tubes refilled with water every one and a half weeks.

Source: Amazon.com
The Bedol water clock also has an alarm and can run for 12 weeks or more before topping up with water. All you need in order to power the Eco-Friendly Water-Powered Clock is a little water -- and a splash of natural lemon juice. This clock runs off a simple galvanic cell battery, which entails the emersion of a cathode or positive metal (such as copper) and an anode or negative metal (such as zinc) in an electrolyte solution. The lemon-laced water serves as the electrolyte solution, which allows the transfer of electrons between the two metals, resulting in an electric cell.

Source: Bedol
An alternative shape is the water powered clock bottle from Ochelly.

Source Ochelly
Although a clock is an extremely small gadget, it still uses power. No gadget is too small to harvest green energy and water powered clocks can be used in rooms that do not get enough light in order to use solar power.
Top image source eroundlake.com