I mostly enjoy Mario Kart Wii's online Battle, despite a few problems that are present. I have played the online battle so much that it unlocked Mii Outfit B.
There are some things that are particularly annoying about online battle– first and foremost, Funky Stadium. I have never disliked a battle course so much. It is simply too big, which makes it impossible to catch up to people, and the constant blockades make it difficult to throw red shells. And somehow, I think the "random selection" done before battle is rigged. I have noticed that if ? is picked, it will most likely be a course no else picked. And if one's selection has the least chance of being picked randomly, it most likely be picked.
The battle rating system has some annoyances as well. It follows a "you gain some, you lose all" philosophy, so several consecutive wins earn like 100 points, but one loss deducts 200. The only upside to it is that I can easily tell who some of the cheaters are, who have 9999 points, so I can drop out prematurely without losing points. However, it does not take into account whether or not your teammates sucked or you were grossly outnumbered. So if your team lost but you had more points scored than the leading person on the winning team, you don't even get brownie points. It's bullshit.
But nonetheless, MKW's smooth online has probably made it my most played game on Wii.