There is nothing as cheap and fast as a pen and paper. That said there are huge drawbacks to pen and paper.
For one thing, in order to use those fleeting notes in a systematic way they need to be organized. And in many cases will need some standard notation system. It could be as simple as writing "todo" at the top of a post it note.
Randomly scribbling stuff on scraps of paper here and there might work for somebody, but even a little system will go a long way.
Obviously once you start using a computer a whole new world opens up.
In my practice I focus on the types of things I need to capture, I make sure I can capture them all using the same tools and also that they end up in the same place.
After I've got them collected, some just stay where they are. Others get processed according to their purpose. For example: I have my tasks emailed to me every morning and my reading list emailed to me on the weekend.