For John Locke and his followers “what makes a person identical with herself over time is her remembering or being able to remember the events to which she was witness or agent.” (According mostly to the followers. What Locke actually said is something else, to which I’ll come back shortly)
Jesse Prinz has another opinion.


In this video Prinz seems to advocate that we maintain the continuity of our selves by sticking to a set of values. But this is only ‘skin deep’.
He didn’t actually say ‘what keeps us ‘together’ over time but ‘what people think that is ‘keeping us together’ as time passes’.
These two are not necessarily the same thing.
The way I see it memories are just the ‘resource’ from which our identity is continuously being built and the ‘values’ we stick to are the ‘blue-prints’ we use/update during the process but that the ‘driver’ behind all this is our self-awareness/free willing soul.
All three are interdependent.
As Locke observed, without our memories we would be like balloons drifting in a cloud of deep fog. We wouldn’t even be able to determine whether we were moving or not.
As Prinz said, without our values we’re like ships which have lost their ‘compass’.  Just imagine a boat sailing during a starless night or in a cloudy day. There are ways that experienced sailors can use to determine whether the ship is moving – relative to the surrounding water – but not even Black Beard nor Magellan would have been able to reach their destinations without ever seeing the Sun, some stars or using a compass.
Not to mention the fact, sorry Jesse, that without our memory we wouldn’t be able to remember today what set of values we had been using yesterday.
Finally, but not lastly, without our self-awareness/free willing soul we would be like perfectly sea-worthy ships which have been abandoned by their crews. Adrift in the middle of the sea, at the mercy of the elements. Elements themselves being not merciless but amoral…
 I’m sure that by now you have already figured out what I mean.
It is “we” that ‘compares’ and ‘considers’ things, that forms “ideas of identity and diversity”, that sees “anything to be in any place in any instant of time”, that is “sure” of anything (or not)… and so on and so forth…
Without this “we” no discussion about memory nor values would have ever been possible
Without memories the “we” would go ‘hungry’. Or nuts.
Without values the “we” would be ‘toothless’. Or antisocial/in jail.
And all these have already been mentioned, albeit in different terms, by both Humberto Maturana and Stephane Lupasco.
Don’t tell me that none of you have ever thought, however passingly, of the other meaning of ‘stool’.