Keyboard shortcut to jump between tabs on OS X Terminal

The key combination is: Shift-Cmd-Left or Right

It can be done from System Preferences > Keyboard > Shortcuts > App Shortcuts > click + > select Terminal.app and add the option title as it appears in the Terminal menu, which can be:

• Select Next Tab (on Mavericks and earlier)
• Show Next Tab (on Yosemite, El Capitan, Sierra...)

Note: As you probably realize, you can do this with absolutely any [Cocoa] OSX app that has a menu with options, even if originally the app defined no shortcut for the option.

This kind of shortcuts are not equivalent to using native app shortcuts. What OSX is in fact doing is triggering the provided menu option via the label - you'll notice that while you press the keys the corresponding menu item will flash in the menu bar.

^{After years of resisting the idea of using a third-party terminal i finally switched to iTerm2 primarily because of properly working window split which in the ootb Terminal.app is not very useful. Also the shortcuts are fully configurable, making it possible to achieve anything you want, including switching to a specific tab with ⌘+[tab number] to jump to the Nth tab.}

Ditch Terminal and use iTerm. It lets you do this and is, to me anyway, a bit more useful.