What I normally use is double-clicking the titlebar of the window. I think now this option may be off by default. Go to System Preferences > Appearance and check the box for "Double-click a window's title bar to minimize". This offers a much larger target area than the minimize button.
A couple other tips that involve adding in the modifier keys along with the double-click action. (Some of these may not work in all apps, or might not be available in older versions of OS X--sorry, having gone through 10.1, 10.2, 10.3, 10.4, 10.4 and 10.5, it can begin to get a bit difficult to remember when which feature was introduced).
Anyway, hold down the Option (alt) key and double-click on the window title bar to Minimize All windows (from the current application) to the Dock. (Option in this context means "apply to all"). Similarly, if there are multiple windows from a particular application that are minimized in the Dock, Option-click on one of the window's icon to have them all brought back out.
As with virtually any command or feature that involves animation, the Shift key can be used to impress your friends. ;-) It causes any animation to go in slow motion rather than normal speed. So, Shift-Option-double-click on titlebar minimizes all windows from an app in slow motion, etc.
Regarding using a single key (such as just pressing M without any modifier keys), no you can't do that as far as I know. Any kind of action like that will require at least one modifier key — (Option (alt), Command (⌘), or Control— in combination with the "regular" keys. The modifier key is needed so that the application can know that it should interpret the letter M as a command, and not as plain text.
Updated:
Here's Apple's list of keyboard shortcuts:
http://support.apple.com/kb/ht1343