OK, lots of well meaning comments on this but some of it may not be 100% correct. That is understandable as the electronic systems on modern cars are so complex and difficult to fully comprehend.
As for the "OBD II Plug" people are taking about. Its a technically a "SAE J1962" connector. Its pin connectors are clearly spelled out by SAE standards. This was to allow a universal generic scan tool to be connected per EPA standards adopted in the late 1980's and fully implemented by all 1996 model year vehicles sold in the US. I have attached an article that spells the pins out for you.
I appreciate those who shy away from using this plug for anything. To be frank, its best to leave things you don't know anything about lone as a general rule. I appreciate and applaud those who wisely follow that rule. For those who are more open minded and pay attention to details, let me lay it out. Pin 16 on the J1962 connector is nothing more than 12V+ battery power. It has no connection to anything (including any computer or other electronic device) in your car other than the Batt + power bus. The purpose of that pin was only to provide the power to operate a scan tool. You can use that pin to power a low draw device without danger of hurting anything unless you draw too much from it and blow its fuse. That said, there are many better options and ways to do this. Rather than have an unknowing person accidentally draw or inject power into the wrong plug why not go to your fuse box and pull your power from there? There are many nice options for doing this including special fuses that plug in and allow your extra circuit to piggy-back another circuit in the car. Since more vehicles have extra sockets anyway due to the various options that might need power but aren't installed in your vehicle you can often find a place for a fuse.
I appreciate the input of "ASE Technicians", especially the one's who are cautious. Much of what they have to say is technically correct. I had many of those guys in class back in the 1990's when we were rolling OBD II out and I had to train hundred of them on how OBD II was going to work. Part of the class was explaining that J1962 connector and how it as wired and functioned. The real problem we most often found with using the J1962 for devices was actually more on the ground side of the circuit. The J1962 has two ground terminals. Pins 4 and 5 are both grounds. BUT, 4 is a chassis power ground for the scan device power while 5 is a "signal ground". Using 4 for a device ground is fine as that is why it is there. However, we saw cases where people were using pin 5 for a ground and that threw off the reference voltages for sensors as this ground is used by the computer for voltage reference.
Like I said, it is technically possible to safely use the J1962 for power and ground for a device but there is a possibility that you could foul up and use the wrong pins and cause "complications" in the system. Play it safe and go elsewhere. That is the straight poop and the best answer you will find.
http://pinoutguide.com/CarElectronics/car_obd2_pinout.shtml
Pin 16 is clean power but honestly, you can find other options with a little search. Its always best if you can power items off the fuse box however.