When is a fuel pump needed on GA aircraft?
On a low wing monoplane you'll need a pump all the time. There will be a mechanical pump fitted to the engine for the purpose. On a high-wing monoplane the engine is often gravity feed.

However, during critical phases of flight (specifically take-off and landing) you wouldn't want to have that fail so a second auxiliary electric pump is fitted that the pilot switches on beforehand and can switch off once that phase is over. 

The Pilot's Operating Manual will give specific recommendations for use on any given type.