I use MAMP everyday, nearly all day to simulate running a server on my Mac. It’s awesome. Once I start up MAMP, I rarely have the need to use the application window. One more window means messier Exposé reveals and more dock clutter. There’s no no need to have it around. But (I believe as a way to incentivize you upgrading to MAMP Pro) you cannot close the application window. This means that the window is always present, either on your desktop, or minimized in the dock.
Here’s how I hide the application altogether: Dock Dodger removes the application icon from the doc. Then hide the window with Cmd + H. If I ever need to get back to the application, I can do it via Quicksilver or Spotlight.
Or just uncheck ‘Stop Servers when quitting MAMP’.