When your badge breaks, it's bad. Be it by gunfight, or by an unnamed bounty hunter saying, "Think you people need a new sheriff." right before taking your badge. Situations like this haunt all men and women of justice, because without your badge, you can't command respect. That badge may be all that stands between you and a Colt Revolver.
My badge recently had the clip break off, thanks to it being cheap and not hand-forged in the Arizona Territory. Hopefully, with this Instructable, you can prevent the same thing from compromising you protecting law and order.

Step 1: Preparation

To begin with, I got the materials needed, which should be on hand. All I needed was a safety pin a little bit shorter than the star was wide, and some epoxy* to hold it down. I was a little worried about epoxy at first, but it dries incredibly hard, and in copius quantities, is even better than the original fastener. Also, since you're using a safety pin the badge will stay on more securely, s definite plus after bumpy miles on horseback.
Rub some sandpaper on the back of the badge to rough it up, and provide a better surface for the epoxy to stick to. Test out some possible locations of the safety pin, and find one that works right for your badge, You'll want to have a little space between the pin and the edge.

*Prettier alternatives: solder, though I'm not sure how secure it would be, and welding.

Step 2: Action!

Now, mix up a copious amount of epoxy. I mixed up a circle about the size of a quarter, or about 2 cm across. Just mix more than you'll think you need, because you will end up using it all. I put a lot of epoxy on, then put the safety pin on (pointy side up), and then put more epoxy on. The pin was covered pretty heavily, which will ensure that it stays on. One thing I forgot to do however, was clean up the outlying splatters. If you don't do that at this stage, it will be impossible to clean up. You've been warned.
I propped the pin up with a penny while it was drying, so that I could actually get it on. Anything will work, but you just want the pin to be near-perpendicular with the back of the badge.

Step 3: Ride 'Em Up!

Now you can go and ride off into the sunset, or break room, either work fine. But keep in mind that you now have to protect justice and right wrongs, and never give into corruption!