Shoot from farther away. Video cameras have great zoom lenses, and if you need to cover even more distance, there are telephoto adapters available. You can shoot from the back of the church or up in a balcony, and still get a nice head-and-shoulders shot of the bride and groom. There are, of course, drawbacks: When shooting at telephoto settings, a tripod is mandatory. Camera shake or movement is much more apparent. Most lenses are less light-sensitive at the telephoto end, so you may have to open up your iris another stop, or add a bit of gain. Also, depth of field tends to be shallower at the telephoto end of the lens (and with the iris open). A shallow depth of field is generally good for image composition, but it means you have to pay close attention to your focus.
Don't use on-camera lights. Most churches won't allow supplemental lighting anyway. In special circumstances, like a candlelight ceremony, try to hide some small lights in the altar floral arrangements. Avoid glaring lighting rigs that call attention to themselves and to the taping activities. While we're on the subject of lights, turn off (or tape over) the red tally light on the front of your camcorder. Use a smaller camera. This is another tradeoff. A big shoulder-mounted camera will usually have a big, professional lens and other desirable features. On the other hand, a small camcorder draws much less attention to itself, and today's prosumer handycams come very close to the performance of the "big guns." Sometimes, extreme measures are in order. One colleague found he and his camera couldn't fit under a chuppah (the canopy used in Jewish wedding ceremonies) with the rabbi and the wedding couple. He mounted a tiny palmcorder on the chuppah's framework, and turned the LCD panel so the bride and groom could see it. They could then use the camera's LCD to position themselves to get a great shot (a matter of moving just a couple of inches one way or the other). Don't move. Once the ceremony starts, don't change position unless absolutely necessary. Many churches insist that you don't move, anyway, since it draws the audience's attention away from the ceremony. Cover multiple positions by using multiple cameras, instead of moving a single camera from place to place. As much as possible, pretend you're a statue. Don't fidget. Have spare batteries and tapes in your pockets, so you can get at them without having to duck down and rummage through your gear bag. Don't gesture to your assistant camera operator(s). Have a radio communication system that lets you talk to them quietly. Discuss with them in advance any special shots you want, such as a closeup from a back camera on the unity candle-lighting ceremony.
Hide in the bushes. You may be able to conceal yourself and your camera partially behind a floral arrangement or inside a box stall pew. If you dress to blend in, you'll also reduce your visibility quotient. If you're up front with the bridal party, this may mean wearing a tux, or at least a black suit. You can even eliminate the distraction caused by a camera operator on the altar entirely, by using a remote-controlled camera instead. In this case, you can be sitting in the back while you control the pan, tilt, focus, and zoom of the altar camera remotely. Your crew should also dress appropriately, even if they're shooting from the back. This is a wedding, and a crew in jeans and tank tops will be a big distraction.
Besides the way you go about getting the shots, there's another aspect to "unobtrusive" camera work: the art of making the viewer forget about the camera. In other words, you don't want your camera work or editing to come between the viewer and the story. Here are some more ways to make yourself "invisible" in the final cut.
Avoid pans. The eye doesn't work like this. Even when we slowly turn our heads from side to side—like a camera panning on a tripod—our eyes move in little jumps from one point of interest to the next. Our eyes work more like a cut than a camera pan.
Avoid zooms. Our eyes don't zoom. Any time you employ a zoom, the viewer's awareness of the camera's presence between her and the image is increased. (Yes, there are artistic reasons to use a zoom. But the downside is this increased viewer awareness of artificiality.)
Use more cuts. As I said, the human eye works more like a cut transition than anything else. Besides, a cut has zero duration; any other transition takes some amount of time and increases the viewer's awareness of the video medium, rather than the message. Do I always follow all of these rules? Heck, no! I've broken every one of them. But I try to be aware of them, and realize when I break one that I'm giving up a little bit of my invisibility, either to the event participants or to the viewers of the finished product.