Sometimes, if you're playing as Luigi and he falls off the track, he will say, "Thank you!" to the Lakitu who rescues him.
In Double Dash!! When you finish the race, the two characters you chose celebrate together. While this leads to the obvious niceness with pairs like Mario and Luigi or Mario and Peach, it becomes really sweet to see Luigi and Waluigi or Mario and Bowser so pleased with each other. Especially during the award ceremony.
In the section right before the cave on Double Dash's Sherbet Land, there are two Shy Guys skating together. It's a small, but sweet sight to behold. Even better, in 8, they'll do tricks.
Meta example: Several fans joined together to play Wii's online one last time together on May 19th, 2014. The next day was the end of the Nintendo Wi-Fi connection, meaning online play was terminated.
If you get the Link DLC, you'll see that he is clearly having the time of his life. The look of glee on his face when he wins is simply adorable. Fridge Brilliance kicks in when you realise that the fastest thing he's ever ridden is a horse - riding a kart or bike must be incredible to him.