Well, since @Bourbon has already done the Vigilante a justice, I’d like to talk about this one. In case if you don’t know, NFS franchise is 27 years old already, you probably can tell its fans’ ages by just asking them which one is the best. I belong to the group which played Underground at first, and will say neon underglow, nitrous, and Japanese imports are cool things.
But then there’s the classic pre-underground era, which includes many beautiful and unmodified 90s supercars too. I’d recommend you to watch LGR’s recent retrospect video about NFS II here, you can tell its major difference from the later iterations.
Also, seeing how Hot Pursuit (I’d assume you meant the 2010 one, not the previous 2) and MW2012 are pretty popular in your poll, I dare say that Criterion also successfully created its own group of NFS fans after they no longer developed Burnout series. Car crash and damage effects are really their specialties. Both games still looks very good to these days. We will have to see what they can do to the upcoming game. It will be a topic created when it’s announced though, so stay tuned. 
Lastly, I’d like to mention The Run. You may think of it as the Absolution of NFS. Both features a linear storyline, linear levels. They both strangely took place at 2011/2012 and during some points, at Chicago as well. Well, that doesn’t sound good, right? No, it literally shut down its developer Black Box, those who made UG and MW05, for good.
However, its sceneries and lighting effects from Frostbite 2 are great! It features plenty of point to point levels across USA before The Crew was a thing. It also remains as the last NFS which doesn’t feature brake-to-drift handling too. In the end, despite the game didn’t offer too much, it will always hold a special place in my mind.
