My favorite FE game, I could probably talk about all the chapters in full detail. So, to go along with what everyone else said:
As said, avoid the center house in and the Wyvern Riders that appear later Chapter 11. There is a unit and a weapon you can obtain in this chapter, though.
Get to the Pegasus Girl in Chapter 3 before the bandits do, and you can recruit her in a later chapter.
During "arrive" missions, you can have every character leave, but only Ike will end the chapter. I forget if something special happens if everyone leaves first, but other than extra dialogue, I don't think so?
In the level with all the priests as enemies, don't kill any of them! The Aether skill can also be obtained in this chapter, iirc. Make sure Ike gets that.
Once you're on the boat after Chapter 11, look through the base conversations with "Unknown" I think it is and you'll get Sothe. Actually, just look through base conversations whenever you can, you get stuff sometimes.
Chapter 17. Four part chapter. Brutal.
In the prison level, don't bother trying to sneak around. Just attack the nearest guard and get some experience.
At the very end chapter, when it asks which character you want to bring in, answer Giffca. Doing so will unlock his portrait in the gallery after the game is completed. Unless you don't care for that, in which case, go with Tibarn.