I love battle animations. The different effects for the different magic types in FFIV are very memorable for me. Summon animations have also been a stable for FF. The lack of battle animations is one of the reasons I'm not as big a fan of the early Dragon Quest games as I am of FF.

Xenoblade Chronicles has some cool battle animations for a modern game. Also the Bravely Default series. The problem with FFXIII's battles is that you have to be constantly paying attention to your inputs that you can't enjoy watching the flow of battle.