Place disposable cameras on the tables at the reception. The guests than can take pictures at their leisure; and I am sure you are going to end up with some nice snapshots. If you have kids at the reception, you should maybe consider not to put out all cameras from the start, since they might run out of film too quickly.
Place a printed note to place next to the camera: “Please help us experience our wedding reception through your eyes. Take a few pictures and pass the camera around. Please leave the camera on the table and we will take care of the rest!”. Make sure to have the MC talk about the cameras and encourage your guests to use them you mingle with them.
Make sure that someone checks if there are any cameras that have run out of film. This person should also collect the remaining cameras as the reception comes to an end. Another idea is to put a basket close to the door for people to drop off the cameras. If the person in charge mails the cameras in for mail-order processing you might even have the pictures waiting for you when you get back from your honeymoon. If you also order a CD with pictures or scan the pictures you can post them on your website or weblog for everyone to see and print.
Don’t be too disappointed - some pictures will not turn out, and some shots might be double - maybe even a camera or two might disappear. You will have some nice snapshots in between.
If you buy the cameras in larger quantities you can often get a better deal. You might want to consider cameras with a flash if the light is dim - however the cameras with a flash are sometimes harder to use:
There are even some places that will provide you with customized disposable cameras for your wedding. Here are some cameras to pick from at CatalogCity:

Wedding Cameras at CatalogCity.com