I believe I once exploited FE7's "mine an enemy into mind control" glitch, leading to some funny justification of their actions. In FE4, I almost screwed myself over by placing Celice WAY too far into Orion's dragon head thingy. That taught me the lesson that it isn't a good idea to send one knight lord into about 12 dragon knights, one of them holding a holy weapon. (Then this.)

In a few maps my Pegasus/Sniper/Cleric would get separated from the group and surrounded by enemy reinforcements, but they usually managed to stay alive long enough to get help or take down the enemies, which takes a while. 

Valkyries in Fire Emblem are good for not being hit whatsoever. With that in mind, in Chapter 16 for FE6, I put Clarine (who is a Valkyrie) in the way of a small crowd, so the big guy in the middle, Douglas, won't get killed (which, apparently, is the way to obtaining him as a character and a way to not kill him). 16 seems to be a hard map-at least, it would be, except for the fact that nearly all the people are bent on killing Clarine. Here is what I have, the neverending queue to try and kill one girl without any weapons on her own.