This depends entirely on the components in the computer.
Entry level (Internet, email, word processing) computers from manufacturers such as HP, Compaq, Dell, etc. have a PSU a little over 300 Watts. Little or no upgrades can be done with these types of computers.
Medium (average) level computers have PSUs in the 500 to 650 Watts range. With these computers, some gaming is possible. Multi-tasking works reasonably well.
High end computers with powerful CPUs will have PSUs from 700 Watts all the way up to 1,000 Watts (some even 1,200 Watts). These computers are for heavy gaming, multi-tasking, and other CPU intensive uses. These computers are usually home-built, or custom built by manufacturers because of the variety of options available.
If you can list the components that you want in the computer that you have in mind, we can come up with a specific answer to your question. Including recommended brands of power supplies.