Q:

Can I tap into an exterior light in order to power a security camera?

I have an exterior light (shown below) that I was wondering if I could tap into, in order to power an outdoor IP cam.  I understand I would have to pull appart some cables and potentially purchase connectors, etc. but I am up for the challenge if it is possible.
Note:  The exterior light is on a switch controller from inside my house.  I would, of course, want the camera on at all times and NOT be controlled by this switch.
My camera:
http://www.amazon.com/Foscam-FI8904W-Outdoor-Wireless-Viewing/dp/B004KVKATQ
My house:  

A:

Chances are good that there is only one cable coming into that light, and it is switched by the interior switch.  If this is the case, as I suspect, you cannot draw power for your cam without the light being on. you will need to find a continuously powered set of wires or run a new set to your cam. 

A:

As Shirlock mentioned, the switched lamp is a problem ... however, there's a possible solution:

replace the light with a fixture that'll switch at dusk.
leave the switched turned on.

You could bypass the switch, but then it's more inconvenient if you need to do work on the circuit.  You can get covers that'll screw on over the faceplate so someone won't turn the switch off by accident.
Also, although it seems like a good idea to get motion detecting light and save power -- it might not be a good idea in this case, as you'd have nto shut off the camera if you wanted to override the motion detector when you want it to stay on.  (most require you to turn the power on, then off, then back on).  If you don't have people visit you at night or order food delivery, it might not be a problem, though.
...
If it were me, I'd likely look at what's behind the switch, and see if it'd be possible to use the existing wiring to feed some pull line into the wall, then pull two cables into the wall, one switched and one bypassing the switch (assuming you're not overloading the circuit by doing this).

A:

I like @Joe's solution actually, but I'll offer another.
You may be able to find another source besides the light. 
From attic
In the attic, you may be able to find a live circuit you can tap into. Put a receptacle in the rafters (above the insulation), and then you can plug the transformer in there, and run a low-voltage wire down through the soffit to where the light is mounted. This is the most discreet option, as you will not see any wires or plugs at all, and your existing exterior light won't be affected. 
From inside
You also could probably find somewhere inside the house to put the transformer, plugging it into an existing outlet, and then run the low-voltage wire up into the attic, and down to the soffit. Just keep in mind that the longer wire you have, the more of a voltage drop you'll get and the bigger a wire you will need. 
You may also have a place where you can simply run a wire straight out through the wall (even if it's not directly where the camera is mounted - eg, if could even be at ground level), and then route the wire around the outside of the house (eg, hidden along the edge of the soffit, along window frames, edge of siding, etc) to the camera. I've done this before while adding satellite TV to houses, and done properly it can be completely hidden.
From basement/crawlspace
You may be able to do the same from the basement/crawlspace if you have one. Find a receptacle somewhere in the basement (or add one along an existing circuit), and then drill a 1/2" hole through the concrete, running a low-voltage line in conduit (PVC conduit is fine) out of that up to where the camera is mounted. Seal up the hole and again, you have a conduit running up, but it's low voltage and you have no transformer/receptacle visible. If you don't have a hammer drill now, this may be a much more difficult option, or a good excuse to buy a hammer drill, depending on how you look at it.

With all of these options, you get the benefit of no exposed outdoor transformer (and the transformer shown in the pic is definitely not designed to be exposed to the elements), and you can also plug the transformer into a UPS (battery backup) so that the camera will continue to work even if the power is out (which is only usful if the DVR or whatever you have it plugged into is also on a UPS, of course). 

