One particular genre that I feel benefits from an ethernet connection is fighting games, where even a tiny fraction of lag can affect gameplay. One game that I'm waiting to see how it performs online is the Wii U version of Tekken Tag Tournament, because a single frame can alter what moves you can punish, what combos you can perform, and so on.
Despite having WiFi-capable consoles, I still use ethernet cables (with the proper ports open) to maximize connectivity.