You have me today, tomorrow you'll have more, as your time passes, i am not easy to store, i don't take up space, but i am only in one place, am what you saw, but not what you see, what am I?

Hmm ...

Memory?

Because:

Today I will live my memory, tomorrow more memories will come. As time passes, memories aren't easy to remember, it doesn't take space, and it's only in one place, which is the pass. Memory is what we saw, but not see anymore.