Is it possible to have tabs in Finder? I often need to open many finder windows at the same time and my desktop becomes cluttered. 

Is there any way to get tabs in Finder so one window can host multiple folders?
Update: As shown in File Menu and being consistent with the rest of the macOS shortcuts, command+T will open a new tab. Tabbed Finder was introduced in OS X Mavericks in 2013.

With the native Finder app that comes with OS X is not possible to have tabs.
If you really need them you can use some Finder replacement app, like TotalFinder or PathFinder (both not free).