Most people would agree that the Euro-game movement has done a lot of good things for game design, but there always seemed to be a gap in the realm of simple attack-your-neighbor's-territory games. A couple war-themed games have utilized Euro-style simplicity (Mare Nostrum and Wallenstein both to great effect), but those lack the purity of something like Risk.
Of course, opinions of Risk among the hobby-gaming community tend to be pretty derisive, and that's somewhat understandable. It's as likely to be six hours long as it is two, and it only really gets interesting with it's meta-game, forming alliances and so forth. So if any genre needed a good Euro-izing, it is the simple war-themed game.