From the experts:
Old-fashioned nickname with sweet turn-of-the-last-century charm that's become a favorite among the popular girl names starting with A of today. In fact, with all spellings of Adeline/Adalynn taken together firmly in the Top 10, and Adelaide and Addison also high in the charts, Addie is one of the most frequently-heard short forms around. But no matter how popular (or pandemic) it gets, Addie is undeniably one of the cutest names for baby girls. Little girls might like the fact that it's the name, though spelled Addy, of an American Girl series doll.