With respect to Polly, I think a raised bed on paving would be fine if, as you say, it's deep enough. But you would need to make it self-supporting or buy one of the kit-form ones. I bought one a bit like this when the local garden centre had a sale on last year (it might be a good time to look abot now!),
http://www.greenfingers.com/superstore/product_review.asp?dept_id=200486&pf_id=LS7672D
I laid sheet of permeable membrane across the bottom and stapled it to the sides to stop the soil washing out of the bottom when watering etc, and lined the sides with heavy duty plastic.
The person at the garden centre recommended multi-purpose compost to fill it with, I was doubtful about this and checked out my feelings with this Board and I'm glad I did. The advice was to fill it with a mixture of bought top soil and organic farmyard manure - not cheap, but it'll last much longer and provide better growing conditions for the plants. I've got fantastic crops already this year, including the best courgettes I've ever grown.