The Folder Options control panel in Windows is a collection of unrelated settings that boil down to this:
General tab. Exactly as in Windows, it’s up to you whether or not double-clicking a folder opens up a second window—or just changes what’s in the first one. On the Mac, you make these changes using the Finder→Preferences command. There you’ll find the option called “Always open folders in a new window.”
View tab. Most of the options here don’t exist on the Mac. For example, system files are always hidden on the Mac; you can’t opt to make them visible (at least not with the built-in controls). You can, however, choose whether you want to see the file name extensions in your desktop windows (like .doc and .html). Choose Finder→Preferences→Advanced, and turn “Show all file extensions” on or off.
File Types tab. Just as in Windows, you can reassign certain document types so that double-clicking opens them in the program of your choice. But on the Mac, you can reassign either a whole class of files at once, as in Windows, or one file at a time. To do it, use the Get Info window, as described in Locked Files: The Next Generation.
Offline files. There’s no equivalent feature on the Mac.