Informal:
* Fais-moi un câlin! (This is the most common and straightforward way to say it.)
* Embrasse-moi! (This literally translates to "kiss me," but can also mean "hug me" in a playful or affectionate way.)
Formal:
* Donnez-moi un câlin, s'il vous plaît. (This is a polite and respectful way to ask for a hug.)
More specific:
* Serre-moi fort! (This means "Hold me tight!")
* Je veux un câlin! (This means "I want a hug!")
It's important to choose the appropriate phrase based on your relationship with the person and the situation.