Actually there are quite a few places in the world with time zones on the half hour:
GMT-9:30 Marquesas Islands(French Indonesia)
GMT-3:30 SE Labrador and Newfoundland (Canada)
GMT+3:30 Iran
GMT+4:30 Afghanistan
GMT+5:30 India
GMT+6:30 Cocos Islands and Myanmar
GMT+9:30 Australia Central Standard Time
GMT+10:30 Lord Howe Island (New South Wales, Australia)
GMT+11:30 Norfolk Island (Australian Territory)
In addition, there are a few with +45 minute offsets:
GMT+5:45 Nepal
GMT+8:45 Caiguna, Eucla, Border Village (SE Western Australia)
GMT+12:45 Chatham Islands (New Zealand)
All times listed are Standard times and don't take into account Daylight Savings Time.