La Sagrada Familia. Designed by the city's most famous architect, Antoni Gaudí, it combines neo-Gothic and modernist styles to create a church unlike any I've seen.
Yet, surprisingly, for all of it's acclaim, the church hasn't been without controversy. George Orwell in his book "Homage to Catalonia" said, "I think the Anarchists showed bad taste in not blowing it up when they had the chance," labeling it "one of the most hideous buildings in the world." More recently, Josep Maria Subirachs's minimalist interpretation of the passion façade brought complaints that it didn't adhere to what was left of Gaudí's original designs, most of which were destroyed by the aforementioned anarchists during the Civil War.
Beauty or monstrosity? I personally think the former and never tire of getting the chance to walk by, look up and marvel for a second while meeting a friend or running errands. So if you're visiting, there are some great hotels close to the Sagrada Familia if you want to stay near by and stroll the tree lined Avenguda de Gaudí, which links the church and the famous Hospital del Sant Pau.