The polymer notes[1] we use in Australia (and also print for several other countries) have been around for about 18 years now and have very low rates of counterfeiting due to the number of security features built in[2].

The notes do cost more to produce, but the extra durability means that they last about 4 times as long (from memory) in circulation, so overall the cost difference is marginal for the government, but is an additional deterrent for counterfeiters.

[1] http://en.wikipedia.org/wiki/Polymer_banknote [2] http://www.rba.gov.au/banknotes/counterfeit/index.html