I'm using an iMac with OS X Snow Leopard 10.6.8 in my office. I don't have a right click option for my Mighty Mouse.
I checked with my System Preferences and I don't have any options to enable "Right Click". I only have Tracking Speed and Double Click Speed options.
It's a bit tough to use without right click buttons on the mouse when I need to press the Ctrl button all the time.