Half hours aren't that special - there are quite a few, and a large percentage of the worlds population is on a 1/2 hour offset, since Indian Standard Time is UTC + 5 1/2. The special cases are the quarter hours. I mentioned the little Aussie one before - there's also the New Zealand territory of the Chatham Islands, whose time is set at 13 hours 45 minutes ahead of UTC, and I think some uninhabited US owned islands in the Pacific have a similar timezone.
These are sparesly inhabited places, so it doesn't matter to many people, but Nepal deserves special mention as being the only proper country to do this. Nepal time is 5h45 ahead of UTC - because why not?