The Streak should never end. I said it 10 years ago, 5 years ago, last year, and now.
To back my opinion, I'll use actual matches and possible matches as examples:
Randy Orton - Wrestlemania 21: This was as of now the best time to end the Streak. Taker was just back as his Deadman gimmick, while Orton was the Legend Killer, and a fresh heel again. He was young, cocky, had only one World Title reign, and even had the RKO to counter out of several spots. Result: Taker won. Orton still came after him, costing him matches and eventually getting the win at Summerslam relatively cleanly for a heel, and a casket win as well before eventually losing in Hell in a Cell. A nearly 6 month feud that put Orton in the upper echelon, since he competed for the World Title in the upcoming Wrestlemania 22, and on from there. Orton didn't need to beat the Streak; only show he was a credible threat to The Undertaker, and defeat him down the road.
Edge - Wrestlemania 24: Edge was undefeated in singles and tag team action at Wrestlemania (he lost a Money in the Bank match the year before) and seemed to have Taker's number in matches. However, the story came full circle for Taker to win back the World Title, but Edge banished him in a TLC match a few PPVs later. He maintained his credibility and didn't need the Streak.
Shawn Michaels - Wrestlemania 26: Shawn was done anyway. He went out just the way his idol Ric Flair went out. He didn't want the Streak. He wanted the one person who could put him in place to put him out.
HHH - Wrestlemania 27 and 28: Fitting revenge if HHH did it? The crowd and the internet would have lost its mind if he did. Taker had to come back for 28 just to get to 20.
CM Punk - Wrestlemania 29: Taker didn't need this one, and it kinda scares me that maybe Paul Bearer's death may have made the decision to keep the Streak a walk in the park. Before it I thought there might have been a chance that Punk would have gotten the opportunity. Still, though, it only made Punk a more credible threat when he came back (albeit with terrible creative booking)
John Cena - ??? - Not unless they turn him heel, and even then, Cena ending the Streak does nothing except antagonize the crowd. Maybe if Cena's first match were against Taker it might be a full circle thing. Cena faced Angle first, though, and while Cena did benefit from a feud with American Bad-Ass Taker, they don't really acknowledge that on-air so it doesn't factor in.
Daniel Bryan - Maybe the only superstar it'd benefit because he'd be an "A" player by doing what HHH, Michaels, Flair, Orton, Batista, and on and on could not do. Still, though, Bryan facing Taker for the Streak would make more sense if Taker were champion, because Bryan's goal is validation that he deserves to be champion, not individual match achievements. Bryan wants the World Series, not the MVP award.
Sting - It'd be such a slap in the face to anyone who put their time into the WWE for Sting to never ONCE be a part of the locker room come in and beat Taker. I seriously think Sting would get the Batista treatment: a part-timer comes in and takes away a worthy spot from other full-timers, leading the fans to turn on him mercilessly. A match? Absolutely. End the Streak? Never. It'd be more venomous than good.
Roman Reigns, Bray Wyatt, any other young up-and-comer - if they're already ready to move up, I'd give him what Orton went through: lose at Wrestlemania and be a part of the Streak, come back and get that decisive win over Taker. That will establish them, because it works.
Overall on the future of the Streak:
I say it'll stays intact and goes either to 25-0, or until Taker can no longer safely and physically compete. I think he'd be glad to lay down for anyone, but he'll never have to. And the year, the month, the day he calls it a career will be a sad time for all of wrestling.
