The best story I have involving zip ties was at the FTC Oklahoma Regional. I was the second round of finals and our ally had taken some heavy hits which knocked one of their key components loose. I asked if zip ties would help and they said yes. So we were allowed a 30 second pit stop to repair their bot before the second match of finals...
Thanks to zip ties our ally's robot worked amazingly well...
If only we had remembered to turn on our robot too... -.-'