Apple don’t make this obvious in Safari’s preferences pane, however after some digging I figured out you can actually switch between tabs using the keyboard:

   <- Switch to Left Tab               Switch to Right Tab ->
Command + Shift + [               Command +Shift + ]

Update: Tha Shell suggested a way where you can configure the keys you want to use to switch tabs…

Step 1: Go to System Preferences > Keyboard & Mouse > then choose the Keyboard Shortcuts tab
Step 2:  Press the + key at the bottom of the window:

Do the same as above, but now type ‘Select Previous Tab’ and assign a key as before.

Voila! you can now switch between tabs with a keyboard shortcut that you prefer. I wasn’t able to get command + right/left to work, if you get it to work, let me know by leaving a message