I am playing on Casual mode, so I don't have permadeath enabled for my characters. If they die, I keep battling without them, but then I can use them in the next battle.
However, I noticed that when Chrom died, I got a game over instead of getting to continue the battle. I assume if my character dies, I will also get a game over.
Are there any other character deaths that will trigger a game over in battle?