It's so they can crush the bottles more easily. With the tops on the bottles don't crush and so take up more space. For the lids or tops check with your local council. I know here in Australia and in South Africa the plastic tops or lids are not being recycled currently. In the UK there are some charities that collect the tops and then recycle them. I assume they work out a bulk deal of some sort.
So the current suggestion is to take the tops off and throw them in your normal rubbish or collect them if you can find a local scheme!
Does anyone know why they can't be recycled with the bottles?
Here's a link for the UK