I bloody love River Song. LOVE.
She's smart, sassy, beautiful and unlike other companions who are - at least sometimes - fawning, over-impressed fangirls, River is a peer of the Doctor who loves him because she wants to, rather than because the Doctor is the only awesome person she knows or because he provides an elite life of otherwise unattainable adventure. River creates her own adventures, she is her own woman, she doesn't need the Doctor like the others do. She's awesome.
Which I think creates a problem with a lot of fans, because she is over-familiar (understandably because she has known him very well from the moment he met her, what with their timelines travelling in different directions) and is on the same or similar level as the Doctor.
I can see why a lot of fans don't like that.
And some fans just don't like Alex Kingston, well there's no accounting for taste, lol.
Her introductory episodes, the Library two-parter, are among my favourite storylines, such a clever concept, so I've loved River from the start. I could have lived without them getting married, I prefer my DW sans romance, but as that ship has well and truly sailed, I can tolerate it because I don't see their relationship having the power imbalance that the Doctor's other 'romances' have had.
And I can't wait to see the dynamics between River and Capaldi's Doctor. Gonna be fun for sure.