Barcelona is one of the densest cities in Europe. And Márton Mogyorósy's recent photo series, called Barcelona from above, does an excellent job of demonstrating that. My favorite photo is this one here, showing La Barceloneta neighborhood adjacent to the beach:

None of the buildings are particularly tall (maybe 6 or 7 storeys at the most), but the streets are probably only about 6m wide, including sidewalks. This is one way that you can achieve density without height and it is a good example of what I was getting at in my post, European-style height, but not density.