The character remembers the past, but ages backwards (so they remember what happened when they were "older").
The character remembers the future, and is exceedingly confusing. This can be a form of Cursed with Awesome—it allows the character to serve as a seer, but if taken seriously more or less precludes them from developing much of a connection with anyone (as just about any event carries the opposite sort of emotional resonance for them as for anyone else). Sometimes characters like this come off as Mad Oracles.
The character remembers the past, but remembers successively less of it as they get younger. Usually this occurs when Merlin Sickness is contracted partway through life, while the other two options are more associated with characters who are "born" (that is to say, who die) with it.
Ah, but I was so much older then, I'm younger than that now.