AV Club recently finished their retrospective review of the new Doctor Who's 2nd Season, which is as far as I've made it into the "new" series myself. Since the theme of the season was the nature and lasting power of 10/Rose's relationship, especially as the season moved along, I figured I might as well do the fashionable thing and chime in on the relationship as well. Granted, it's been several years since the season was initially released, so I doubt I'm going to break any new ground here, but better late than never, I suppose.
At its core, Rose's relationship with the 10th Doctor was pretty straightforward - he's an older (about 700 years older, more or less), well-traveled gentleman and she's a young, impressionable woman. Rose loves the Doctor in a near-obsessive, all-consuming way, the way a teenager falls in love with someone. She wasn't just willing to sacrifice her previous life - her family, her friends, her job, her neighborhood, everything - for the Doctor, she actively encouraged him, practically begging, to take her up on it. The 9th Doctor was reluctant to do that; he cared for Rose the way an father-figure or an older brother might, at least until the end, and attempted to preserve some distance between the two. The 10th Doctor, however, actively reveled in the attention in the same way that a 40+-year-old millionaire might appreciate the unbalanced devotion of a pretty 18-year-old - he enjoyed the way she made him feel, the way she encouraged instigated his long-forgotten, more youthful tendencies (hence the running gag with Queen Victoria in "Tooth and Claw"), and rewarded her accordingly.
Unfortunately, at least for Rose, the Doctor had 700 years of perspective to draw from. He could never feel the same way about Rose that Rose felt about the Doctor because the Doctor ultimately had a life outside of Rose. Rose's entire existence had become co-dependently wrapped around the Doctor's - she lived exclusively for him. The Doctor, however, had a life before Rose and he knew that he would have a life after Rose. Sooner or later, the relationship had to end, either through death, boredom, or Rose getting sucked into a parallel universe. The writing was on the wall after the "The Girl In The Fireplace" - as fun and eager and complimentary as Rose might have been, she would never be an intellectual equal to the Doctor, someone that he would be able to look at eye-to-eye and experience attraction from that connection. When the Doctor found the Madame de Pompadour, and when she clearly expressed interest in him, his reaction was not that of a man guilty of betraying a lover but instead a man lost in a desert, enjoying a rare, satisfying drink. Without the Doctor, the Madame de Pompadour was still the mistress of the King of France - Rose, however, saw herself as nothing without the Doctor and they both felt that acutely.
In the end, for Rose's health as well as the Doctor's, the relationship needed to end. Rose needed an opportunity to discover that there is life after the Doctor, though I wouldn't be especially surprised if, like a lot of people that endlessly yearn for a particularly intense, lost love, she never really recovers. The Doctor, meanwhile, needs someone that he can respect and can look him in the eye, someone that can hold him more or less responsible for his actions.
Now to see if he finds that in season 3.