I follow the directions on the ubuntu website (http://www.ubuntu.com/download/desktop/create-a-usb-stick-on-mac-osx) to create a bootable USB stick. I then restarted my mac and tried to boot up the USB stick. I get to the screen that ask if I want to install ubuntu or try ubuntu. I selected the try ubuntu and I see the ubuntu screen and then a black screen. This black screen lasted until I turn off my mac. I left the black screen on overnight.
32-bit PC (i386) desktop image: For almost all PCs. This includes most machines with Intel/AMD/etc type processors and almost all computers that run Microsoft Windows, as well as newer Apple Macintosh systems based on Intel processors. Choose this if you are at all unsure.
Based on this, I suggest downloading the 32-bit image from the mirror of your choice. Beyond that, I can suggest a boot parameter which might help, but I can't explain why. Getting Ubuntu working on my own Mac was a very trying experience.
EDIT: If you decide to try, the boot parameter which helped me was nomodeset, as shown here. Again, I don't understand why this worked for me, so no way to know if it will help you or not.