Multiband base station antennas include first and second arrays. The first array has a plurality of radiating elements that are arranged in a plurality of columns and rows, where both an uppermost and a lowermost of the rows of the first array include a first number of radiating elements, and at least one of the other rows of the first array includes a second, larger number of radiating elements. The second array includes a plurality of radiating elements that are vertically offset from each other. At least one of the radiating elements in the uppermost of the rows of the first array is not vertically aligned with any of the radiating elements in the lowermost of the rows of the first array.