Not sure there is any definite answer to this. Some of my friends have sterilised and still do even though their children are 18 months old. For me I thought I wasn't going to worry after 6 months, but in fact kept sterlising utnil about 9 months (although if I just had to wash by hand on occaision that didn't worry me). I just used the dishwasher to wash them after that.
Milk residue is the perfect culture medium for bugs (more so than general household dirt), and can be difficult to clear from teats. So my view is to only sterilise or use a dishwasher as long as you are giving milk through a teat.
Anything else including sippy cups used for milk and bottles used for water, I take apart (including the valve if there is one) and use a hot wash with soapy water, hot rinse and air dry.
I thought current official UK guidance was to sterilise bottles until a year (when you should stop using bottles anyway really). Formula is the perfect medium for bacterial growth as beamel says, so a bottle teat is far more likely to harbour bacteria than a dummy dropped on the carpet. Especially as formula may be contaminated anyway if you don't make it up with hot water.
DD is 6 months and I've stopped sterilising toys, dummies and spoons but still sterilise bottles, teats and storage pots for my EBM as the EBM can be in those for a while.