General:
* Scribble
* Scrawl
* Dash off
* Jot down
* Write hastily
* Pen furiously
More forceful:
* Scrawl
* Scribble
* Dash off
* Rattle off
* Whirl (used more for writing with great speed and energy)
More formal:
* Compose rapidly
* Write expeditiously
Other options:
* Speed writing (refers to a specific type of writing competition)
* Note-taking (implies writing quickly to capture information)
* Drafting (implies writing quickly as a first step in a larger writing process)
The best word will depend on the specific context and the tone you want to convey.