So after the river card is turned and bets are made with a call from player 2 to player 1. Player 1 shows the cards and presents the winning hand. Player 2, who called the pot then says you win and just throws the cards in face down. Can player 1 ask to see player 2's cards since the pot was called and player 2 did not fold?
Casinos may have different house rules, but the "standard" rule is this: since the hand reached showdown, any player involved in the hand may ask that player 2's hand be shown. If anyone except player 1 asks, the dealer will pick up player 2's hand and make a show of touching it to the muck to emphasize that it is a dead hand, then show it.
If the ostensible winner, player 1, asks to see the hand, the dealer will make no such motion, the hand will be shown, and it will be live. Player 1 therefore asks to see the hand at his own risk.
The ostensible reason for this "all called hands may be shown" rule is so that players can protect themselves from collusion: player 3, for example, might suspect that player 2 mucked the winner after building a pot for player 1, his confederate. But players do abuse this rule, so it is not at all uncommon for casinos to restrict it, or for floormen to refuse in some situations.
It varies from casino to casino. Typically, yes you do, although some rooms are moving away from that rule or are disallowing players from asking to see mucked hands, if they abuse the rule.
Primary source: Wikipedia poker showdown
From my experience, it is only enforced that the last aggressor must show first then the others may muck. In your scenario, player 2 would not be obliged to show.
Herb's source ( Wikipedia's 'Showdown (Poker)' ) implies that there can be reason to view a mucked hand if there is some suspicion of cheating or siding. Despite this,
"players do not have an inherent right to view mucked hands."
So It is not correct to say that this is a requirement.
As for your question:
Can player 1 ask to see player 2's cards...
Yes, player 1 can ask. But player 2 has no obligation to show their hand in this scenario; many players (myself included) will muck their losing hands to avoid disclosing information about their range and play to the other player(s). Otherwise you are unnecessarily just feeding them information that they could use against you.
If you call someone, you can ask to see their hand before deciding to muck or show yours (at cash). If someone calls you, then they can ask to see your hand before they muck or show.
The poker etiquette way is to both showdown at the same time, but this almost never happens.