They actually add a filter to cameras to block out / lower the amount of IR light captured, or all your pictures will have a pink tinge. A quick way to test, get your TV remote, start recording on your camcorder, and point the TV remote IR led at your lens (holding a button down), if it lights up it will capture some of the IR range.
On ebay you can find premodified cameras to allow the full spectrum for about $150 from China. (They remove the filter from the CCD.)
Here's the kind of pinkish photos you can expect from it; on my Flickr stream (and pics of my IR light array)
DarkIR | Flickr
You can also pay to have your camera converted (for quite a hefty price, but many camera specialists offer this service) eg:
LifePixel Digital Camera Infrared IR Conversion And Modification Services. Frequently Asked Questions.
Also there are guides across the net on how to convert specific cameras to allow full spectrum, but they are not for the faint hearted.
Edit: Model of Camera I use if you want to search Ebay for one: SVP T718 HD camera