You say "Happy Birthday" in Spanish as: ¡Feliz cumpleaños! If you want to be more formal or add more warmth, you can say:

• ¡Feliz cumpleaños a ti! (Happy birthday to you!)
• Te deseo un feliz cumpleaños (I wish you a happy birthday)

Let me know if you want it in any specific Spanish-speaking country's style or with a special phrase!