Siliconera is reporting that in the console versions of King of Fighters XIII not only can you save your replays, but you can also potentially upload them for the world to see -- as long as you don't suck, that is. Apparently there is a certain criteria that must be met in ranked matches before the game will allow you to upload your replays. While there are no details of what is required to upload replays, it probably has to do something with amount of supers used in a match, perhaps HD combos that were completed -- stuff like that.
Also, they mention each player will have their own profile card that shows how you stack up against your friends, how much of the game you have unlocked (trials, gallery) and how much time you've currently sunk into the game.
The King of Fighters XIII comes out at the end of October and you should get it because it's a fun game to play and is pretty to look at.