Even though relentless1 already mentioned this one, a real feud between Goldberg and Sting would have been amazing. I always felt that Goldberg's streak should have been ended by either Bret Hart or Sting.
I can only recall seeing two matches between Sting and Goldberg, and one of them didn't have a clean finish. The first was when Sting was in the Wolfpac (red face paint), and it main-evented an episode of Nitro. Goldberg was World Champ at the time, and the match's finish came when Sting had Goldberg locked in the Scorpion Death Lock. That's when Hogan entered, and clobbered Sting over the head with the title belt. Somehow, the ref just plain "didn't see it" (I don' think it was a matter of the ref being "knocked out", I think it just happened "outside his field of vision" somehow). Goldberg hit the jackhammer, and got the 1-2-3.
The other match was when Sting was World Champ at Halloween Havoc in 1999, and I believe he was a heel at that point. Sting called an "open challenge" to anyone in the back, and Goldberg came out to answer the challenge. Goldberg defeated Sting for the belt, even though the announcers didn't seem to understand why the belt had changed hands (leave it to the failing WCW at that time). I think the title change was later reversed, due to the match being "unsanctioned"...something like that.
I think this feud would have worked even with both Sting & Goldberg as faces, as it could have been booked as a "Franchise vs. Franchise" match. That would have been big enough to main event Starrcade, and sell the PPV on it's own. I would have GLADLY paid the PPV money just for that match back in 1998/99. I really wanted to see Goldberg's streak end with him tapping out to either Sting, or Bret Hart. I don't know why, but the Scorpion Death Lock/Sharpshooter just seemed like the move to beat him. IMHO, I feel that Goldberg's first loss should have came from some type of submission hold, and not the lame "no DQ" finish that it ended up being (Scott Hall using the taser, and Nash getting the pin). We all know how much MORE lame that storyline became, as well.
I would have also loved to have seen a rehash of Jericho & Goldberg, when Goldberg first showed up in the WWF. They had their little "joke feud" in WCW, with Jericho bringing out "Greenberg" (WCW's "Gillberg" at the time). When Goldberg showed up in the WWE, it would have been great to see a "real" feud between the two of them. Jericho had "proved" that he wasn't a cruiserweight anymore by that point, and the matches between those two could have been epic. The very beginning of the feud could have mentioned their "history" in WCW, with Jericho having "video evidence" of him pinning Goldberg back in WCW. That would have been hilarious! Too bad Goldberg didn't stay long enough with the WWF, as they definitely had a lot of other "dream feuds" for Goldberg during his WWF run. The Jericho/Goldberg feud would have been entertaining though, at least in my opinion. If it were to happen, I'm sure there would have been no way that Goldberg would have agreed to jobbing to Jericho. Maybe I'm wrong, but it just seems that way to me.