Obviously, his WrestleMania III match with Hulk Hogan, which is possibly the most famous main event of all time. While fans know that Andre's final years were wracked with serious pain as a result of gigantism, Andre actually had to have serious back surgery done in order to compete in this match, and had to wear a brace under his singlet. Andre went through with all this just so he could put Hogan over on the big stage. Talk about a Determinator.
In a CMOH for Vince McMahon, of all people, McMahon researched the surgery for him, convinced him to do it, and paid for it out of his own pocket without Andre being required to do the match.
In an equally CMOA for Andre during the surgery, and also related to the "greatest drinker in the history of mankind" thing mentioned above, the anesthesiologist in charge of the back surgery had no clue how to treat a giant beforehand. Finally giving up, he merely asked Andre how much alcohol he drank in one sitting. Andre replied "It usually takes me two liters of vodka just to make me feel warm inside". The anesthesiologist used this as a guide for how much to give him, leading to a medical breakthrough that's still used as a baseline for people with gigantism today.
Even better? When Heenan slapped him, and Andre recoiled in shock, the crowd started to go nuts because they knew what was going to happen.
There are plenty of great Andre stories. Such as when a group of drunks would not leave him alone. So, he went after them. The guys, thinking they were bright, jumped in their car and locked the doors. Andre then proceeded to tip the car over with them all still inside.
Michael Hayes told the story of how he and the other Fabulous Freebirds showed up late to a show. Andre happened to be the agent and was very agitated. Hayes, known for it, pitched a tantrum, saying he'd go right to the top. Andre said that was fine and that the next day, either they would be gone or he would be. The Freebirds were sacked.
Rob Reiner recounts a tale in which Arnold Schwarzenegger and Andre, who had forged a friendship, being both enormous, European transplant badasses in the entertainment industry, happened to be in the same city at the same time and went out to dinner together. Andre was famous for insisting on paying for dinner with everyone he dined with. In an attempt to subvert the Giant and pay for the meal himself for once, Arnold called the waiter aside and asked for the bill. Andre responded by picking up Schwarzenegger (at the height of his bodybuilding days, no less) and carrying him back to the table like a small child. Talk about moments when you wish you had a camera.