My wife had a small plastic flower where the main stem had a wire in it for shaping, but the off-shoots were just plastic. One of them broke (indicated by the arrow). Typically just gluing it would not be strong enough to hold for very long. I came up with a solution that might help some of you.
Step 1: Broken Flower
I don't have a picture of it when it was broken, but if you can imagine the cross section was just a solid plastic stalk.
Step 2: The Solution --> Special Soldering Iron Tip
I used an alligator clip to hold a small piece of copper wire (other wire and other fastening method could be used) and cranked up the heat on my soldering station to 850F, since I knew the wire would be slightly cooler than the actual tip. I used this wire tip to gently poke into each end of the broken spot to hollow it out so I could insert another piece of wire into the holes then join the stem back together. Then I used the wire tip to gently melt the sides of the stem around where they were joined together. I just tried to make it smooth like when working with clay and the result is seen in the pictures on step 1 and the intro.
With the wire inserted, it helps make the joint stronger, and by melting the stem around the joint and keeping it smooth, you don't have the gaudy appearance of glue all over the place.
Hope this helps someone in need.
Edit 9-28-2014: added a new pic to show a slight modification. Rather than just clamping the copper wire with the alligator clip, I wrapped the wire around one of the jaws. Now it is easier to add to the soldering iron when needed.