Generally the answer is no - conservatories can usually be erected with the minimum of fuss and paperwork - However planning permission will be needed if:
The conservatory exceeds 50 cubic metres in volume (or 10% of the houses original volume) if built on to a terraced house or 70 cubic metres (or 15% of the houses original volume) for other types of house.
Any part of the conservatory is within 2m of a boundary.
Any part of the conservatory projects beyond the existing front wall or is higher than the highest part of the roof line.
The property is in a conservation area or is listed.
The property has been previously extended.
The conservatory would take the extended area to over 50% of the garden.

This list is not comprehensive and you should always check with your supplier or local planning authority. Rules differ outside England and Wales.