Right now, Command+Tab and Command+Shift+Tab cycles between windows. How can I rebind this to use Alt instead of Command?
I'm looking for a native solution which doesn't require 3rd party software.
I am assuming you're an experienced Windows user, based on a few things in your question. First, command+tab doesn't actually cycle between windows (like it does in Windows), rather, it activates the Application Switcher. Cycling through windows in a single application is done with command+` and command+shift+`.
This behavior can be edited in System Preferences -> Keyboard -> Keyboard Shortcuts under Keyboard & Text Input (on 10.6).
I don't believe you can rebind the only the Application Switcher to alt+tab, but you can rebind the command key entirely to option, if you chose. Also in the Keyboard System Preferences, this is in the Keyboard tab; click the "Modifier Keys..." button to show a sheet allowing you to change modifier bindings per keyboard.
On a Mac keyboard, assuming you're using one, however, the command key is in fact exactly where alt would be on a PC keyboard, so I can't think of a good reason for wanting to change this. Maybe you're using a PC keyboard with a Mac, in which case reassigning alt to command with the "Modifier Keys..." sheet is exactly what you're looking for.