Not my favorite set of years for horror, but I'll do what I can for my fellow GOG member. The movies that stick out in my mind for horror are as follows (I'm not including movies with horror elements that are basically comedies or action movies) ;

Catacombs - The plot and atmosphere are pretty compelling. The action takes place in France where raves are conducted in under city tombs and follows an American tourist who's been invited over by her sister.

Ruins (Unrated) - Pretty much college kids vs dungeons and dragons man eating plant in Mexico. Good plot.

Lake Mungo - This one takes place in Australia. It's presented like one of those supernatural documentaries you see on cable. The plot is intriguing in the sense that it's a more traditional ghost story then you get in cinema. Don't expect gore but do expect a good plot and very creepy moments.

Borderland - Based on a true story. College kids go to Mexico for spring break and get caught up with the local drug cartel who also happens to be a cult devoted to some esoteric South American god. The plot and horror reveal are pretty good here.

Pulse (Japanese Version) - This is a strange film. It starts being one of the most frightening films about ghosts haunting the internet and ends with an apocalyptic series of events. I can't say the plot is good as I have the other films, however the watching experience is unique and at least half the film will have you hiding under the covers or your significant other holding onto you like white on rice.

The Mist - Stephen King movies were hit or miss in the early days and seemed more miss in the post 2k years. That being said, this is an exception. The plot is very engaging and has a well done twist at the end. I won't spoil the plot with a synopsis but suffice it to say that it marries plot elements from Doom (the PC game, not that horrible film) into a well made cinema piece.

The Cell - One of the earliest films that meet your criteria in my collection. It's one of the few films I own that actually has J-Lo as the lead. The plot is engaging and follows the adventure of a psychologist who is using an experimental hardware to tap into dreams to help people with psychological issues. The scenes are pretty amazing to go with that engaging plot.

Signs - I can hear the sighing now. Really an M. Night Shymalan movie? Yes and here is why; the movie has two story's in one plot and it's done well in an engaging manner. I haven't seen a film execute the two story plot successfully after that until Super 8 came around.

Paranormal Activity (just the first one, don't bother with the sequels) - Pretty much the spiritual successor to the Blair Witch project. This time around, the story and plot revolve around a couple in a modern house where a haunting is going down. So much better lighting this time. The plot is engaging and there are a lot of jump scares. A lot of people down this film for it's spartan use of effects and jump scares. I feel that if Alfred Hitchcock were alive today and decided to do one of his rare horror films, it would be in this vein (maybe the plot would be off the charts but it would be done like this)

Jeepers Creepers - This film is pretty much one of the best classic styled monster flicks of the modern age. The plot is engaging and has quite a few frighting moments. If your wondering why the film gets low stars on rating sites, many people protests the directors involvement in the film (he was involved in one of the worst crimes a human being could be involved in). That being said the plot is engaging and the monster is something you will be frightened of.

The Strangers - This film is one of the best slasher films in your time range. The plot is engaging, has bump scares, and can get really intense.

Masters of Horror (showtime series of films) - I recommend the following Heckel's Tale, Imprint, Incident On and Off A Mountain Road, Deer Woman, Cigarette Burns, Jenifer, Pelts, Dream Cruise, Pro-Life, Dreams in the Witch House

Dagon - A lovecraft tale done by one of the best directors of horror, Stuart Gordon. The plot is engaging, the shock and gore does not disappoint and the horror is top notch.

Ju-On - This started the whole craze for Japanese horror in the early 2k years here in the states (well this and the Ring). A good old fashioned ghost story well told.

The Eye (Korean version) - This film follows the life of a woman who gets a newly developed surgery to allow her to see again. It works but not without a very odd side effect. Pretty scary.

Donnie Darko - This movie is so bizarre and plot so engaging. Some might argue that this is not horror, but I think it qualifies since the possible time travel element is disturbing to a lovecraftian level that results in the main characters demise. Great performance and plot.

Trick 'r Treat - I didn't have high hopes for this film. The film is actually a set of vignettes set to a main plot that is mediocre, but the individual stories are engaging, shocking, gross, and scary.

Drag Me To Hell - One of my favorite tongue and cheek directors, Sam Rami tries his hand at horror and scores awesome. Here we have a woman who tries desperately to rid herself of a gypsy curse.

Pandourum - A nice marriage between sci-fi and horror. Engaging little tale on space cabin fever.

Seventh Moon - One of the key parts of horror is having the main character feel isolated and this film hits on that horror tone in spades. A woman goes with her fiance to his native homeland and gets trapped in a backwoods community with a dark secret. Engaging plot and pretty scary stuff.

The Descent - Speaking of vacations going bad, this is probably one of my favs of the bunch. This has all the elements of horror done well, isolation, character perma changed (besides traditional death), gore, people becoming monsters in their own way.

The Maid - A woman from the phillipines goes to do maid duties for money out in China during a spring festival honoring the dead. This is a well done horror film.

Suicide Club - This is a more human bent on horror. A fad of suicide grows across Japan and the story follows a detective trying to figure out whats going on.

Battle Royal - Same humanish angle of horror except this time it's a lottery of sorts for students and survival show.

The 3 Extremes - A vignette of three stories that are probably the goriest I've ever seen.