A classic "Shoe Goo" glue can do the trick if your rain boots get holes, cracks, or leaks. Put some duct tape on the inside of the boot where the hole is, then fill the outside of the hole with the glue. After about an hour, remove the tape from the inside of the boot. Some alternatives to try are a silicone-based aquarium sealer, rubber cement, or Stormsure adhesive.
If your boots are higher quality or expensive, it might be a better idea to bring your damaged rain boot to a cobbler.