Lots of amazing games mentioned, and glad the '96 College WS final got some love. Warren Morris's HR is one of the most climactic ever... 2 outs, bottom of the 9th inning in a winner take all championship game, and LSU was trailing at the time of the HR. Very few, if any game ending HRs meet all those criteria.
https://www.youtube.com/watch?v=NXtP385K9dE
I won't argue with any of the others listed- Game 6 '86 WS, Game 1 '88 WS, 1992 Duke v Kentucky, etc, but below are a couple amazing finishes that got a bit less exposure.
1994 Plano East v John Tyler for the Texas state title is still maybe the most ridiculous finish I've ever seen in any sport, on any level. I remember seeing highlights on Sportcenter when it happened.. I was a senior in high school, maybe a week or two after having played my final football game, and it left quite an impression on me at the time. I remember trying to explain what I'd seen to people, in the days before YouTube, and would guess 9 out of 10 thought I was exaggerating or just completely full of it. Was happy to see it get a little play on ESPN this past year due to it being its 20th anniversary.
https://www.youtube.com/watch?v=ZHkABO0VwCg
The other is just an awesome college hoops finish, Adam Spanich USC, 6 pts in 2.8 seconds vs Oregon.
https://www.youtube.com/watch?v=fkWOxWX4GP0