For some players, holding onto a blue shell can turn into this. The lead cars will often panic and stop dead in their tracks.
Baby Park from Double Dash!! might be That One Level due to items bouncing all over the place, but you can't help but laugh at just how chaotic it can get.
In Wii and 7, playing as a regular character or as a Mii and seeing your own Miis in Coconut Mall is pretty hilarious as well. Especially since they also drive the parking cars that you must dodge at the end.
Doing badly in a race can trigger some pretty funny reactions from your racer.
If you play as Wario and he gets lower than Sixth place, he will loudly grumble, "I hate you." In 8, he'll say "Gahh, I hate losing!", and in Double Dash? "I lost! To a bunch of losers!"
In Wii and 7, if you rank low enough, Bowser will grumble out a coherent "Horrible..." One of the few moments in recent years (outside of Bowser's Inside Story) where he actually talks, rather than just roaring and grumbling.
The general, yet subtle act of the characters staring at each other as they pass adds so much hilarity or excessive dramatic tension to exchanges that need to be put in slow motion to last any more than a single second.