Kagame Uchiha: He's one of the only plot theories that doesn't cause any real plot holes, mostly because he hasn't been featured in the manga enough to cause any contradictions. It's a case of "less is more". He's the same age as Hiruzen and Danzo, which is pretty old but not feeble and infirm. Danzo, for instance, still was pretty spry. Kagame, like most elders and high-ranking members of the Uchiha clan, would have had all sorts of access to the Naka Shrine tablet, would have known secrets of MS and EMS (and Izanagi), and would have had access to historical records so he would have known which families would produce MS abilities like Kamui that would be beneficial.
Izuna Uchiha: Obviously has the same plans and goals as Madara. Didn't have his own sharingan eyes, so he had to go out and "borrow" a pair from somebody else instead. Madara would have had to bring him back to life with Rinnegan or Zetsu magic, which is odd but not impossible to explain. If he brought Izuna back to life during the second world war, and he was the same age as when he died (pretty young) that would explain his current age and how he doesn't appear to be 100 or older. Madara and Izuna were both described as having exceptionally powerful chakra, which explains why Tobi can seemingly spam different versions of Kamui, while Kakashi can barely cast it a few times before he passes out. Plus, he's a real Uchiha so unlike Kakashi he can use sharingan more efficiently anyway. Who else better to impersonate Madara convincingly, than a person who was from Madara's own family and has many of the same powers as Madara?
Fugaku Uchiha: Was mysteriously missing the night of Tobi's attack on the village. He was old enough then to play the part, and 10 years later he could plausibly have the kinds of wrinkles that we saw Tobi have. He's also taken a special interest in both Sasuke and Itachi, allowing and even encouraging both of them to join Akatsuki (even if he suspected Itachi of being dishonest about it, and trying to protect Konoha or even passing intelligence back to them). He's even acted proud of the two brothers on different occasions. Fugaku actually planned the Uchiha coup, which lead directly to the massacre, Itachi's defection, Sasuke's mentality as a revenger, and many other events in the manga, which is the kind of thing that Tobi/Madara would have wanted anyway. Where this fails is in trying to explain why Mikoto was also missing the night of Tobi's invasion (coincidence, or is she also involved?), and explain how Fugaku faked his own death at the hands of Itachi. Considering that Madara, Tobi's mentor of sorts, also faked his own death convincingly it's not hard to imagine that Fugaku could have done so as well. The fact that Fugaku and Mikoto were inexplicably missing during the night of Tobi's attack is the single biggest piece of evidence here, and is also an extremely interesting mystery that demands some kind of explanation.
Obito Uchiha: Lots of people love this theory, but I really don't think it's plausible. He's the wrong age, he never had access to the Naka shrine, he was born after Nagato had been given the Rinnegan (or even shorly before, it doesn't matter), he would have never met Madara in person, he had the will of Fire, was good friends with Kakashi and never once acted like the kind of maniac who would try to take over the world. Also, he got smashed by a huge boulder, and I have to believe that would leave a scar or two, which we never saw on Tobi. The only real "evidence" for this theory is that Tobi clearly has Obito's eye, and the syllables of "Tobi" and "Obito" are mostly the same, but rearranged. From everything I've seen, that is just a translation issue, not an artifact from the original japanese (I could be wrong here, I don't read Japanese). The only reason Kishi may do this is a lazy way to push the story forward faster, without having to waste a lot of time on explanation. If you're going to be lazy, do it all the way.
Others: I still think it's possible, but less plausible, that Tobi could be an as-yet unnamed Uzumaki. Somebody who Madara met during his travels. Considering how much he knows about jinchuuriki seals (the most advanced of which, Kushina's was an Uzumaki invention), how much he knew about Konoha security (the Uzumaki were a close military ally of Konoha), and how he would have ever known about Nagato and how Nagato would have been a good recipient of the Rinnegan. Again, I used to like this theory more, before the "borrowed power" line. I think it's also remotely possible that he's some other non-uchiha. The fact that his forehead was covered with a bandage and now there's a third hole in the forehead of his most recent mask certainly seems suspicious to me (A branch-family Hyuuga, for example, would have had a seal on the forehead like where Tobi's bandage was, but that doesn't seem a likely explanation to me).
The fact that he refers to himself as "no one" suggests that he has discarded a previous identity. The fact that he took the name of Madara and pretended to be Madara, and even spoke about Madara's actions in the first person ("I fought Hashirama", "I faked my own death", "I am Madara Uchiha", "These are the powers of Madara Uchiha" etc) suggests some sort of fanboyism or self-delusion. Also, the fact that Tobi stayed in his "Tobi" character before he revealed himself as "Madara", even at times when it was just him and Zetsu alone (and Zetsu should have known who it was) suggests that maybe he really IS nobody, he has no personality of his own and he is always acting and always pretending to be somebody else, to the point that he even convinces himself. We can get into a pit trying to figure out the psychology of a character based on things that might be translation errors, especially if Kishi hasn't had a consistent vision and has introduced some weird inconsistencies over 600 chapters of manga over the course of many years. so I won't go much further into this idea. But you get the idea.
There are a few other ideas that make some sense, but I think the three most plausible explanations are either Kagame, Izuna or Fugaku, in that order.
Kishi, first post here too! 
