Informal:
* Любимый/любимая (lyubimy/lyubimaya): This translates literally to "beloved" and is the most common and affectionate way to call someone "sweetheart." It's used for both men and women, just change the ending to match the gender.
* Дорогая/дорогой (dorogaya/dorogoy): Meaning "dear," this is another very common and affectionate term.
* Солнышко (solnyshko): This translates to "little sun" and is a very sweet and playful term for "sweetheart."
Formal:
* Милый/милая (mily/milya): This translates to "sweet" and is more formal and less intimate than the other options.
* Любимый человек (lyubimy chelovek): This means "beloved person" and is a very formal and polite way to refer to someone.
The best translation will depend on your relationship with the person you are addressing and the context of the conversation.