BigStage is definitely one of those services. It uses three photos of your face to map your features onto a virtual head using technology developed for the CIA. Your magic head is rendered into various scenes from popular movies, television shows, and digital shorts--including clips from The A-Team. You can then send those clips to your friends, parents, and relatives to be thoroughly confused and/or entertained by your shenanigans.
The service was originally demoed at both CES and the Under the Radar conference back in June, and made its formal public launch earlier Wednesday. I gave it a spin this afternoon and it managed to transfer shots of my face into what the service calls an "@ctor" in about a minute. After it's done mapping you can tweak various appearance elements from a rather simplistic Flash-based editing tool. I found it to be maddening in that it makes you scroll through each set of sunglasses, hairdos, and accessories page by page. After using something like Spore's Creature Creator, it feels decidedly old-school.
You can save each set of customizations as its own @ctor, each of which can be inserted into video clips with a single click. You can make changes to your character on the fly and see them updated live. To share a video it has to first render you in, which takes about three minutes, although the link to send it to someone else is immediately available.
Another company that's doing this is Gizmoz with its "be a star" feature. The big difference is that BigStage has a much wider range of clips from popular TV content whereas Gizmoz has a small selection of original content and music videos. That said, there is a downside; you must first install a small piece of software to use BigStage, and it only works with PCs running Windows XP or Vista.
I've embedded a sample clip using my face below. If you're having trouble seeing it you can also check it out on this page.