Ooh I LOVE the Saw series! Well, minus the last two. But Saw VI is such a fantastic movie, very underrated.
Some of my other favorites:
28 Days Later - gosh it's just so good. Everyone copies that music for a good reason.
You're Next - The protagonist in this one is so boss I just...can't. She's amazing.
The Blaire Witch Project - As a camper, this always gets me. I could watch it a million times.
Don't Breathe, Get Out, and Hereditary are my favorites of the more recent stuff. Each had me squirming. Watching Don't Breathe with a theater full of men was one of the most hilarious viewing experiences I've ever had, and Hereditary... stunning.
If we're counting sci-fi I'd also add Aliens, Event Horizon, and Annihilation. EH gave me nightmares when I was younger.
Ugh I love horror so much.