This is a difficult question to answer because it very much depends on the size, duration and technical complexity of the project, as well as how many people are involved.
Some projects have been successfully run by a project manager "keeping it all in his head". That may be fine, but when the project manager falls sick so does the project! If you are managing a project for someone else (your client) then at a very minimum you should plan on ways and means to track the definition of the client's requirements and/or assumptions made, the standard of quality agreed upon that will serve the client's purpose, the time available for completion, and the budget for the work.
As projects increase in size and complexity, increasingly sophisticated systems and procedures are available to track each of these core functions. On even larger projects it may well be necessary to have trained and dedicated staff attending to each function separately.