Korodzik: Removed a vast amount of examples which fit more on the Super Star page. Remember, God Mode is about cheat-based invincibility.
Final Fantasy VII had a spell called "Shield," which made the character invincible for a period of time, which was actually pretty lengthy. Additionally, Aerith's Great Gospel limit break induced this status in all party members after completely restoring their health, curing them of all negative status ailments, & even bringing them back from the dead. Too bad you don't get to use it much. Maybe she was killed for being that other kind of God Modder?
"Shield" does not protect from non-elemental damage or items. Great Gospel causes a different effect, "peerless," which does block all incoming damage.
A few enemies in Crisis Core also use a spell that causes invincibility. Also, there are a variety of ways where a character can become immune to physical & magical attacks, but certain abilities aren't classified as either one, so they really don't count as a God Mode.
Similar to the Final Fantasy VII example above, Breath of Fire 3 featured the "Resist" spell which made the caster invulnerable for one turn. It was useful on Fragile Speedster Rei, as characters with high speed often got extra turns in the Turn Based Battle System. Some enemies also used it, potentially causing you to waste certain limited-use attacks.
Final Fantasy VIII has an item called a Hero Drink which allows a character to become invincible for a moderately long amount of time, while another item called a Holy War give this effect to the entire party. What makes this a Game-Breaker is that it is relatively easy to obtain 100 of each item immediately (as long as you invest time into the card game side quest), making a game already full of Game Breakers even easier.
The catch with the invincibility inducing items is that they also prevent status changes, good or bad. However, cast Aura on all three party members, then reduce their HP to 1, then use Holy War, and it's a war indeed...
Rinoa has a random chance of casting this effect when you use her Limit Break and get "Invincible Moon".
Arcane Shield on Spiderweb Software's series Avernum is ALMOST a god mode, but there's a slight chance certain kinds of attacks will go through, everything else either bounces off or hits for 0. It's almost as if instead of being a full shield it occasionally flickers off to conserve energy... Also instead of disappearing completely more and more attacks simply slip through in each consecutive turn. Sanctuary renders you totally invulnerable but you lose it upon retaliating. Similar to the Buddha mode above.
And on a similar note, shields in the tabletop wargame and space sim versions of Renegade work this way as well. The fluff states that fully encompassing shields are only available on larger capital ships due to the enormous power requirement. It is implausibly unfeasible to have a shield like that on tiny corvettes or fightercraft. Therefore, they have flicker shields instead, of which there are two kinds. One encloses the ship, but flickers on and off like a burning out light bulb, while the other is a permanent shield which stays on all the time but rotates quickly around the ship, or can be pointed in a certain direction, though that runs the risk of turning the dogfight into a slugging match as the typical response is to do the same, then sit in front of each other and fire like mad.
Although Overlimit was part of the Tales Series for a while, Tales Of Vesperia's Overlimit Level 4 grants complete invincibility: you won't take damage, no enemy can stun you, you don't consume TP, you can instantly cast spells, you can chain any and all attacks to each other seamlessly, and you have access to Mystic Artes. Sounds awesome, right? Too bad your enemies can use it too.
Then there's using Forcefield and an ability that has a tiny chance of making any buff stick permanently...
The fusion spell "Valhalla" in Persona 3 (available by having Odin and Valkyrie in the same party) grants the target one turn of invulnerability... and then reduces them to one hit point on the next turn. A later-acquired fusion spell, "Infinity" (gained by having Vishnu and Ananta together), grants the same effect to the whole party and takes no toll afterwards. Required for the Bonus Boss.
Korodzik: Removed a vast amount of examples which fit more on the Super Star page. Remember, God Mode is about cheat-based invincibility.