This relay drives me crazy
Your problem is very simple. You are using your breadboard incorrectly. The top pins (pins 1 and 8) are being shorted out by the contact strip. In this case, the breadboard is incompatible with the relay. The spacing between rows of contacts is 0.3 inches, which is a standard DIP IC pin spacing. Your relay, however, has a lateral contact spacing of 0.2 inches, and so cannot straddle the row separation. Since it didn't fit that way, you plugged the relay in to a set of holes that did fit, and that is the source of your trouble. 

To confirm this, set up an LED and resistor to monitor your +12 volts. Unplug the relay and you will see that the LED lights up. Now plug the relay in and the LED will go out. 

With this breadboard you really have no good way to mount the relay. If you have access to a soldering iron you can make extenders for the relay pins with short wires and plug them into the breadboard, but other than that I'm afraid you're out of luck.