People tend to think of time zones as being all adjusted by the hour, but as this clock shows there have been, and still are, exceptions. All of these, were official times at some point.
Sandringham time is the name given to the idiosyncratic alterations that King Edward VII made to the timekeeping at the royal estate of Sandringham. This time corresponds to UTC+0:30, and was used between the years 1901 to 1936. His aim was to "create" more evening daylight for hunting in the winter. The King ordered that all the clocks on the estate be set half an hour ahead of Greenwich Mean Time. In later years the practice was also observed at Windsor and Balmoral Castles, but was thankfully abolished for the ridiculous confusion it caused.
Amsterdam time, or Dutch time, UTC+00:20, was used in the Netherlands from 1909 to 1940.
Bombay time was set at 4 hours and 51 minutes ahead of Greenwich Mean Time (GMT), and lasted from 1884-1955.
Since 1986, the time zone of UTC+05:45 is used in Nepal, of which Kathmandu is the capital.