This seems to be quite a common thing with courgettes, mainly at the beginning and end of the season, it may be temperature related.

The affected fruits are usually a darker green than the others and rot back from the blossom end.

Unless you are experiencing crop failure due to this I would just cut them off and bin them. Courgette plants are so prolific that you can discard a few duds and still have more good fruits than you can cope with.

i've had a few courgettes go like this but its nothing to worry about. just keep watering and soon you'll have more than you can eat.

Make sure you don't leave the faded blossoms on the end of the fruit after the fruit start developing properly - the blossoms rot easily and particularly towards the end of the season the rot easily spreads back into the fruit.