I never have, here in the UK they have to be kept indoors and out of draughts or all the bracts fall off.......beautiful cheery christmas plant,
happy christmas Gwenyth

Are you worried about pollen? No need to remove them at all.

The plant will shed its bracts when the flowers have released pollen, so you could be prolonging the display of the bracts by removing the flowers - might look odd though as there will no longer be a centre to display.

I have had the bracts stay colorful for months, as long as the plants don't get too warm, Urbanite, so the pollen shedding info may not be the whole story. I have never seen any need to remove the florets, myself. It must be interesting getting Poinsettias for Christmas in Oz, though. Entirely the wrong season for them to bloom, though they are all "forced", nowadays.

Thanks, Tug. I took the getting warm into account - it's a Mexican plant and Gwenyth is in Australia so I'm presuming the plant has completely different growing conditions to the sorry specimens on offer in the UK. It may be in something more like its natural climate and therefore may flower and shed pollen naturally and it has shed the pollen it no longer needs to attract insects so the plant will dispense with the colourful bracts.
Poinsettia is sold here as a 'disposable' pot plant in place of cut flowers at this time of year; no-one really expects them to last much beyond mid-January.