Several different moves have saved me in a battle before. One of the more important ones is when I set up Stealth Rock and all 3 layers of Spikes and manage to take out their Rapid Spinner before they can spin the traps away. This usually puts an opponent's Pokemon in KO range for my hard-striker on the team (Kyurem or Cloyster being the ones that do this on my hail team).
Other moves worth mentioning include Will-O-Wisp (when it decides to hit and cripple physical attackers), U-turn (as it helped me in many situations send out a counter when I needed it), Recover (when it gradually restores HP while they run out of PP), Substitute, and Wish.
I did a random wifi match on PBT. I had Armaldo, Dewgong and Feraligatr. My opponent had Dialga, Milotic and Blaziken. So first that Dialga killed my Armaldo and Dewgong. Then I killed it with my Feraligatr. He sent out his Milotic and used Rain Dance to boost his water attacks. My Feraligatr only had 64 hp left when I defeated that Milotic. And then he sent out his Blaziken, did Blaze Kick because he thought he could finish me with that. Because of the Rain Dance it only did 30hp damage and then I ohko'd his Blaziken with Hydro Pump.
Confuse ray has honestly saved me countless times. I remember fighting lance with only my crobat and feraligatr . My crobat took out both of his dragonites using confuse ray along with fly . This gave me the advantage of if confuse ray did not hit I had an escape route. Plus I could keep chalking up damage.
The other day I was battling on PO, on the first turn my Alakazam got knocked down ot 1 HP and I made some bad predicitons and ended up behind my opponent. After some lucky hits, I evened the odds, and it ended up being Tyranitar and 1HP Alakazam against his Latias. Latias knew recover, and spent almost 20 turns recovering and using 4 or 5 Calm Minds before KOing Tyranitar. With nothing else to do, I sent out Alakazam, congragulated my opponent, and clicked Shadow Ball. I had given up on winning, so imagine my suprise when Shadow Ball gets a critical hit, and KOs Latias from about 75% health with 4-5 Clam Minds under her belt.
It wasn't actually the attack alone that saved me. I was battling my cousin when I had Samurott left and he had a Braviary. I used Ice Beam which left it on the red bar and he suddenly uses Grip Claw or something near to that and Samurott almost fainted until Rocky Helmet hurt the Braviary and finished it off ^_^