Harry Potter > LotR > Hunger Games > Twilight
The only series I haven't read in its entirety was Twilight, I think I got maybe halfway into New Moon before just putting it down and never coming back to it. I guess I can't offer a very informed critique on Twilight, but I would imagine that the books getting worse and worse to the point where I just gave up is testimony to how I felt about them. I will give it this, it's better than the insane number of copycats spawned from its genre in the wake of its popularity.
Harry Potter and Lord of the Rings are definitely my favorites. One series might have traits about it that like while the other might do those traits in a less impressive manner. Lord of the Rings definitely gets dry from time to time and I feel like each book is less impressive than the previous. Even though it isn't technically part of the series, I loved The Hobbit, it was this great sort of old timey adventure story that I feel outshines a lot of its modern counterparts. Fellowship of the Ring was good, but this is when the books really started just sort of muddling about and taking forever to do anything. I managed to finish the series, but I honestly wasn't super enthralled with with Two Towers and Return of the King as I was with The Hobbit. (and Fellowship, to a lesser extent) I can see myself rereading Fellowship of the Ring from the series proper sometime in the future, but I don't think I would ever want to tackle the second and third books ever again.
I put Harry Potter first because I enjoyed every book in the series, some more than others, and I was never truly bored with the series. There's a huge cast of characters to know and because they are written from a modern mindset, I think it's easier to connect to them now than characters from an older series. At least on a superficial level. Harry Potter is the series that got me into reading and so it's always going to have a special place with me, but I do think it's a genuinely good series. Solid characters, exciting stories and I've always loved the world setting created in that series. These are books I reread quite often, even the heftier ones that could use some trimming.
The Hunger Games are...decent. I thought the first book was okay, really liked Catching Fire, and just sort of didn't care about anything happening in Mockingjay. The final book has the problem I think the Return of the King and Two Towers had: it takes too long to get anything done. Nearly the first half of the book is Katniss being stripped of everything that made her such a powerful character and we're left with this...emotionally numb thing that I just don't care about. And for all its buildup, the ending was pretty lackluster. Both the epilogue and the end of the war.
My roommate, however, had to read it for a university course
There...are courses the require Twilight readings? Oh my.