I wasn't a big fan of 5, the plot was a bit predictable. 6 was a bit better, and I thought of it a little more as a gears of war type game than a resident evil one.
Though I will say I do like nemesis.
I haven't played all of the RE games, the first one released 2 years before I was born. From the older ones that I have played, I did like umbrella corporation quite a bit. Most people don't though.
However, RE4 is still my favorite. It does implement the camera angle shift which I liked, but there was this mysteriousness of it and the aspect of returning to areas via different routes that I really enjoyed.