The end of season four was very, very controversial. When I first saw it, I felt cheated. I was angry. The more I think about it, the more I think I see what Russell Davies was doing. He is too good of a writer and the show is too carefully crafted for him to screw up Rose's character and the end of a four season storyline. So while the ending isn't strictly part of our series, it is tangentially related, and I've agonized over that scene in Bad Wolf Bay so much that I have to write about it. :)
To briefly set things up, near the end of the final episode of season four, there is a meta-crisis, that results in a part human. part Time Lord Doctor being generated. He has all of the Doctor's memories, and thinks and acts like the Doctor. However, importantly, he only has one heart and cannot regenerate. He only has one life to live. The meta-crisis Doctor brought full resolution to the battle fought against the Daleks, and in the process, wiped them out. Thus, the real Doctor takes him to Bad Wolf Bay in the parallel universe to exile him. He's guilty of genocide. By staying in the parallel universe, the meta-crisis Doctor will not have access to a TARDIS and hence won't be so dangerous.
There's more to the Doctor's decision, then that, though. Even a TARDIS-less Doctor would still be capable of holding incredible power, and a Doctor born in battle and who had just committed genocide would be very dangerous. The Doctor himself was quite violent, and in large part, the larger story of the first four seasons of Doctor Who is the taming of the Doctor, the taming by Rose and Donna. What better motivation for reform could the meta-crisis Doctor have but a lifetime with Rose?
This is a gift for Rose, too, though I'm sure she doesn't realize it. The Doctor makes explicit his desire for her to reform the meta-crisis Doctor. This will act as a check on her, and will prevent her from sliding further into a militaristic lifestyle. On the other hand, there is a sense, too, in which it's an exile for Rose. It's overlooked that she too committed genocide (in season one).
By forcing them to stay in the parallel universe, it also causes the union between Rose and the meta-crisis Doctor to be permanent. There's no point at which she could re-think her decision and try to abandon him for the real Doctor. I think we need to ask, though, why she was willing to stay with the meta-crisis Doctor. It's very clear that she doesn't believe he's the real deal. While I want to avoid doing too much psychologizing I thought I might throw out some suggestions.
The meta-crisis Doctor offers less risk, stability, and the opportunity to be the only one ever. Travelling with the Doctor is dangerous and Rose had already been separated from him once. Who knows, if she goes back to travelling with the real Doctor, she very well could lose him again. The bigger piece, though, is that she gets exclusive rights over the meta-crisis Doctor. As Donna points out, he's part human, they'll grow old and die together. There will never be another one after Rose. I believe it's these factors plus the firmness of the real Doctor's decision and the short amount of time she had to work with that make her decision to stay with the meta-crisis Doctor.
This, lastly brings us to a concluding question about the Doctor. One still has to ask why he made that decision. He was willing to bring the Master along as his prisoner, why couldn't he come up with an arrangement for the meta-crisis Doctor? That would enable him to bring Rose with him too. Perhaps it would have been too hard on the meta-crisis Doctor to see Rose and the real Doctor together. Perhaps he still would be too dangerous in his home universe. It's a sad day for the Doctor and I think a day that revealed weakness on the part of Rose, but as an ending I think it works, even though it broke my heart in a much worse way than did the first scene of separation at Bad Wolf Bay, the place of Rose's and then the Doctor's worst days.
 Exclusion from the TARDIS is never said to be why the parallel universe is a less dangerous place for the meta-crisis Doctor, but I can't think of any other explanation. However, supposedly, in a scene that was cut, Rose and the meta-crisis Doctor were given a piece of the TARDIS, so that they could grow their own. if that's true, though, then I don't see what the point in exiling him to another universe is. It's better to consider it a wise omission on the part of Davies.
 The omission of Martha is deliberate. See my earlier post on Martha for reasons why.
 Rose also was the only option because of the effects that the meta-crisis had on Donna.
 This is a major issue in at least two episodes, School Reunion in season two and the Family of Blood in season three. The Doctor won't settle down with any human because he'll outlive them.
 The decision to force Rose to stay with the meta-crisis Doctor was intensely painful for the Doctor. And I think it likely that she could have prevailed on him if she had tried. I will explore this more with the help of some additional material from the specials between seasons four and five at some future date.