I haven't watched the series in over a decade so I have no idea how it's aged (or how my tastes have changed as I've aged) but I remember the early seasons being quite good. Gray's Anatomy was really popular the first few years that it aired, and at least at the time I thought it was deservedly so. I think I dropped the show around season six? It was getting too soapy/ridiculous and the plot was starting to go in circles. They ratchet up the tension really high pretty early on (both on the medical drama and doctor-relationship drama sides) so the writers inevitably set themselves up for failure, because this isn't a shonen power fantasy, you can't just keep driving things up to higher and higher stakes and still remain within the confines of reality.
For instance, in a very early season there's a really bad train crash where a bunch of patients flood into the hospital and I remember it being a huge climatic thing with some fantastic episodes. Then in a later season they have a bad ferry crash plotline that falls flat because they already did the train crash, and the emotional impact of this huge public transportation disaster was significantly diminished by a sense of "didn't we go through this already?"
I cannot believe that the show is still going, mostly because I'm amazed they have any audience left.