River is fabulous. A lot of that is because she's the human equivilant of a Time Lord, so she can think rings around most everyone she meets. It would be shocking if she weren't arrogant. The Dr, the Master and Romana all share that characteristic with River, so she's hardly the first person on the series to have that quality. I think the Dr loves River, but it's still shocking to think of them having a true romantic relationship since the Dr's nearly always been asexual in his behavior. Even with his deep love for Rose, he never seemed to see her as a viable partner. River is his equal in many ways so he relates to her on a different level. As the last of the Time Lords, River is as close to his own kind as he can get. That has to play a part in their relationship, but I think that Alex K brings enough beauty, charisma and sex appeal to make me believe the Doctor loves her.
I do think some criticsm of River is because she's such a powerful female, and that brings out judgement from some people. Not all River haters are going to have that hang up, but I think some do. When she's judged for having traits that other male characters share without criticsm, it looks sexist.
