Numbers 6:24-26 is a benediction often used to bless a loved one on a special day. Hebrew priests traditionally bestowed a blessing on people each morning at the temple following a sacrifice. Today, many churches end their services with this blessing as a benediction.
Other biblical passages people use include: Proverbs 9:11, James 1:17, Psalm 118:24, and Psalm 20:4. Proverbs 9:11 specifically identifies God adding years to the lives of people. Some use the verse as one of blessing, while others use the verse to poke fun at the birthday man or woman. For instance, a card might say that God promised to add years to the person's life and that God had kept his promise since the person is so old.