It is not necessary to make any skill checks unless the character is under the effects of a memory altering ability or spell (see Memory Lapse) or an affliction that affects his memories.
As the GM, you decide if it makes sense or not if the characters know something.
While it may seem logical that Intelligence decides what a character remembers or not, keep in mind that even animals with 1-2 int scores, a modifier of -5 on intelligence checks, will remember things. Everyone that can "learn" can remember things, you remember how to use your feats, you remember how to use your skills, you remember how to cast your spells. A sorcerer with 1 int (by ability drain for instance) still remembers what his spells do and how to cast them.
Memorization is not keyed to Intelligence, but Intelligence governs reasoning and logic. Which is why wizards prepare (they don't memorize spells) using their Intelligence, but clerics will prepare using their Wisdom and paladins using their charisma. While a sorcerer memorizes his spells known based on how well she knows herself. All of them are "memorizing" things so they can use up later.
If a character really requires a check to remember something, and it does make sense that they could forget it, these are the abilities i would use for each kind of situation:
- Remember a date (he said 24th or 25th?);
- Remember a number (im sure we had to pick up either a thousand or a hundred of those...);
- Remember a name (we met the guy once and that was a month ago...).
- Remember things that are common sense:
- the sun goes from east to west or west to east?
- how many hours are in a day?
- what are the dangers of travelling at night?
- where do babies come from?
- Do note that most of these, the players would easily answer, because they are common sense. But probably not if the player is a young person.
- Remember things that are intuitive:
- i am stuck in a maze, now what?
- we will starve to death, how can we find food?
- that guy on the road with his sword draw looks dangerous to me?
- Remember things related to their character:
- what was the name of my mother? (if it happens in real life, it happens in the game)
- when was the last time i had a bath?
- when is my birthday?
- do i like pork?
- Remember things related to people close to their character:
- when was my mother's birthday?
- who is my best friend?
- who is my worst enemy?
The DC? Probably around 5 or 10. Never higher than that unless it was about a complex topic, but those are better governed by Knowledge skill checks. For instance, remembering basics tenets of your deity is a DC 5 knowledge (Religion) check.