Some candidates:
Kei Nishikori - Turns 25 in December so is really in his prime. As stated, his big issue is staying healthy and, um, Novak Djokovic, Rafael Nadal, and Roger Federer, not to mention Andy Murray and the rest. I really like Kei's "Baby Sampras" game, but I'd still say his odds of every being #1 are less than even, probably far less. Still, if he's healthy for an entire year AND some of the other top players run into some bad luck, then he could do it.
Andy Murray - The clock is ticking for Andy. Who knows, maybe he'll rage back next year but he's on a similar timeline as Novak and an all-around inferior player. Unlike Rafa, Andy doesn't seem to be able to use set-backs as fuel for a rise to the top. Andy is already competing with Guillermo Vilas as the best player never to read #1.
Grigor Dimitrov - He's got the talent but perhaps not the head for it. He could be his generation's David Nalbandian, although he still has a ways to go to be as good as Daveed. He's still "only" 23, so he's got about half a decade of prime years to go so I'm not writing him off yet. While some (i.e. Kieran) are disappointed with his performance this year, let us not forget that his ranking has risen substantially each year since going pro: 493, 288, 106, 76, 48, 23, 11. Maybe next year he vies for the top 5-6, and the year after...well, that would be as good a year as any to grab the #1 spot. I still like his chances a tad better than Kei's.
Milos Raonic - of the "Big Three" of his generation--along with Nishikori and Dimitrov--Raonic has perhaps the lowest ceiling, but we shouldn't undersell him. He keeps making small improvements, which are reflected in his year-end rankings over the last few years: #13 in 2012, #11 in 2013, and #8 this year (assuming Marin Cilic doesn't have a massive comeback at the WTF, the Milos would finish no lower than #9). But its harder to imagine Raonic as #1 than it is Nishikori or Dimitrov. A perfect storm would have to happen: The current Big Four would all have to subtantially decline and/or be injured, and none of his peers--or the up-and-coming next generation--would have to rise to the challenge. Regardless, Milos will be around for years to come, waiting for his chance at greatness-by-default.
Nick Kyrgios - It is easy to overrate Kyrgios because he beat Nadal at the US Open, but its also probably easy to underrate him. He has the talent to be a top 5 player and, at age 19, has a lot of room to grow. Finishing this year at #52 is nice for a 19-year old, but I'd like to see how he does over the next two years. Elite players tend to be in the top 10 by age 21-22, so he's got plenty of time, but he if he's going to get to the top he can't stall out.
Borna Coric - See Kyrgios, but more so - younger, more unproven, but also possibly more talented. Coric just turned 18 so is very, very young and still quite far away from being an elite player. But finishing the year in the top 100 is a nice feat for an 18-year old and he has a legit shot at being a top 20 player by his 20th birthday.
Outsiders: Tsonga, Berdych, Wawrinka, Del Potro. All worth mentioning, but none with a real chance at it, in my opinion.