You can't name just one. There have been several deserving of the top spot.
Austin vs. McMahon - This took the WWF to new heights. Austin/Foley, Austin/Taker, Austin/HBK, Austin/Kane - doesn't matter. All of them, in one way or another, went back to Austin vs. Vince. McMahon was the biggest heel in wrestling for years. Some look back and cry about him being more important than the wrestlers. Fuck off. Seriously. He was the most popular because he was the best. Period.
Austin vs. Bret Hart - This isn't remembered the way it should be. Their match at WM13 is talked about constantly, but their feud was insane. No feud before this felt as personal or real. Their matches were never anything short of outstanding.
Bret Hart vs. HBK - Looking back, this is the most personal feud, obviously. At the time, it wasn't as intense, because we didn't know what was going on behind the scenes. Lasted for two decades, most of that time with both men nowhere near one another. That's pretty epic.
WCW vs. the nWo - There were some awesome singles feuds involved (Hogan vs. Sting comes to mind), but company vs. "company" was the main idea. It took WCW from TNA status to WWE status. I don't care if they stole the idea or not, it worked. I don't care how badly it stunk after six or eight months, it worked.
Hogan vs. Andre - I don't necessarily prefer this feud over the others listed, but you can't deny its impact. They headlined in front of the biggest crowd American wrestling has drawn, and Hogan was the biggest wrestling star on the planet. Andre... well, he was Andre - a total freak of nature who scared the piss out of fans who feared for Hogan's life. Huge, huge deal.
Honorable mentions:
-HHH vs. Randy Orton
-Cena vs. The Rock
-Hogan vs. Savage
-Flair vs. Sting
-Hogan vs. Warrior
-Savage vs. Warrior
-Bret Hart vs. Bob Backlund