How can I remap windows and alt keys in OS X?

Upd 04/29/24:
Apparently the fruit company has been screwing around with the whole Preferences interface for some number of system versions (most of which I'd skipped over).

On macOS Sonoma, v14.4.1:

• Open System Settings (which looks nothing like the former System Preferences and not much like any previous way of doing such things).
• Search for 'modifier' and click on 'Customize modifier keys' (because this item is not listed in the left sidebar - ?!).
• Select a keyboard (if you have more than one). The modifier keys' mapping works like it used to (now that you've found it)!

My previous answer, below, is correct for macOS Monterey (12.x) and earlier versions:
In System Preferences | Keyboard | Modifier Keys you can swap these two (and any other) modifier keys.

Under the Keyboard System Preferences pane there is a button for "Modifier Keys" which allows you to remap command/option/control on a per-keyboard basis. There is no need to use an external tool to switch the keys.

I'm using OSX El Capitan and Microsoft Sculpt keyboard.

This question still pops up when searching today. Steps seem to have changed slightly in newer versions of macOS.

You need to go to System Settings > Keyboard

Click on Keyboard Shortcuts... then select Modifier Keys

Make sure you have selected the right keyboard from the dropdown on top. From there, you can manually swap Option key to be Command, and Command key to be Option.