Unless you count The Blair Witch Project or The Descent as "monster movies," but when I think "monster," I think "big."
The Blair Witch Project never actually shows a monster, but The Descent is surely a monster movie.
My favorite is definitely Jaws. I think it's the best monster movie ever made. The way it doesn't show the shark in full view until the last half hour or so is one thing, and the incredibly strong cast of characters is another. Too many monster movies nowadays have me rooting for the monster by putting in an extremely annoying protagonist (Cloverfield is one of them), but the characters in Jaws are all easy to empathize with, and easy to like.
The remake of The Thing is a good one too. The victim imitation aspect is the best part. It's been done before in films like
Invasion of the Body Snatchers, but The Thing captured all of the characters paranoia and distrust like no film I've seen before. And, just like Jaws, it has strong characters.
Another favorite, and one of the first monster movies, is Frankenstein. In fact, pretty much all of the classic universal horror films are favorites of mine. But, Frankenstein holds up just as well today as before. It brings fright, suspense, and sadness to the screen so well today that I only wish I could've been in the crowd of people that saw it back in '31. I almost forgot to mention
Abbot and Costello Meet Frankenstein as a favorite as well; one of the funniest movies ever made.
There's a few of Dracula flicks out there that I love. Including the 1931 version, the first Hammer Horror version, and even the remake starring Gary Oldman is one that I feel captures the classic horror spirit just right.
I talked about liking The Thing above. As far as Alien films go, to me, only a few can beat The Thing, and one is Alien. A while back, I stated that I think it's the most perfectly paced film of all time, and I stand by that statement. Alien is a perfect example of a great monster movie. Aliens is a great example of what genre bending half way into a movie can do. Alien 3 and 4 may not be the best, but I still enjoy them.
The original version of King Kong is a good one. A prime example of what you can do with film, and still one of the most original monster movies ever made. I loved the '05 remake as well.
A more modern one that I loved was The Mist. It has all the makings and inspirations of a classic monster movie with a strong touch of emotion (something that most creature features lack).
The Elephant Man is a strange one. Not strange because David Lynch directed, but because it's a monster movie, and the monster is the one that's being frightened, not the other way around. The monster is actually the protagonist in this one.
I also have a ton of monster movie guilty pleasures that fall under the
Sasquatch sub-genre, starting with Hammer Horror's The Abominable Snowman.
I'm tired of typing, so I hope that just a list of other favorites will suffice:
Abbot and Costello Meet Dr. Jekyll and Mr. Hyde, The Invisible Man, The Mummy
Dr. Jekyll and Mr. Hyde ('20, '32, '41)
The Invisible Man
Island of Lost Souls
The Phantom of the Opera ('25)
Predator
The Quatermass Experiment
I Walked With a Zombie - Do zombies count?
The Wolf Man
I'm sure there are more that I'm forgetting.