Reanimating a creature with undying
It will not have a +1/+1 counter.

We never actually move an object from one zone to another. Instead, we create a new object in the new zone and the old one ceases to exist.[CR 400.7] Any counters on the old object ceases to exist along with it.[CR 121.2]
That means the card in the graveyard (a new object) doesn't have the original +1/+1 counter. If you use Raise Dead to return that card to your hand, the card in your hand (yet another object) won't have the original +1/+1 counter. And finally, if you cast that card from your hand, the new creature (a fourth object) won't have the original +1/+1 counter.
But does it gain a new +1/+1 counter from undying when you recast the creature card after getting it back from the graveyard using Raise Dead? No. Undying is a triggered ability that triggers when a permanent with Undying is placed into a graveyard.[CR 702.92a] It is not triggered when a card with Undying is cast from your hand, so it doesn't add any counters in that situation.


121.2. Counters on an object are not retained if that object moves from one zone to another. The counters are not “removed”; they simply cease to exist. See rule 400.7.
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are nine exceptions to this rule:
702.92a Undying is a triggered ability. “Undying” means “When this permanent is put into a graveyard from the battlefield, if it had no +1/+1 counters on it, return it to the battlefield under its owner’s control with a +1/+1 counter on it.”