Here are some of my favorites from the 2000's (can't remember all off the top of my head but here goes):
Dawn of the Dead(2004),
[Rec],
Pulse,
Silent Hill (both movies),
Resident Evil series,
Jeepers Creepers 1 & 2,
The Descent 1 & 2,
Ghost Ship,
Primal,
Wolf Creek 1 & 2,
Dale & Tucker vs Evil,
Wyrmwood: Road of the Dead,
Cabin Fever (only the first one, 2 & 3 are a waste of time viewing),
Ginger Snaps,
Dog Soldiers,
The Thing,
The Crazies,
It Follows,
You're Next,
Oculus (not the strongest out of this bunch but was unique. Worth a watch at least),
Mirrors.
That's all I can remember for now and sorry if some were mentioned earlier.