Many classical algorithms, which run in ~O(poly(n)) can have an 'equivalent' quantum algorithm in ~O(log(n)) - an exponential speedup. There is still debate as to how the complexity class of problems which are efficient on a quantum computer (BQP) relate to other complexity classes. Its suspected P lies entirely within BQP.
However, at least initially, I think quantum computers will be a specialized piece of equipment. Classical computing is pretty good for your average person. Quantum computers will be used for more heavy compute tasks.