I'm surprised no one has mentioned the original Dawn of the Dead. It has a healthy mix of action and horror and is very b-movie, but it's definitely entertaining. It's got a different tone than Night of the Living Dead, but that's not a bad thing, and the infamous "political" undertones of the original aren't really there (do expect lots of jabs at consumerism though). Tom Savini plays a small role, in addition to his primary role of designing the zombie makeup, and he does a good job of stealing the scene.
The movie's action elements are a bit toned down--after all, the film was a low budget movie. There are actually times you might feel sorry for the zombies as well. The movie does a pretty good job of reminding you that the characters are in real danger, even when you get sucked into the "coolness" of their behavior. And it establishes relatively early on that none of the cast is safe from death. Despite this, it's one of the earliest zombie movies to actually develop a female character--we see her go from "nearly useless" to "quite genre savvy" over the course of the film.
The gore isn't spectacular by today's standards, but it was notorious at the time for nearly netting the movie an X-rating. There is one particularly hard to watch scene near the end, although hardcore horror fans won't be too upset by it. I wouldn't really call the film a gorefest, suspenseful or scary, but it's a classic for a reason, and pretty much every zombie movie since has drawn cues from either it or its predecessor.
My recommendation on Romero's Dawn of the Dead: well, you won't find it (legally) online. At least not for streaming. However, if you can get your hand on the Divimax DVD, you'll get one of the most complete cuts. You'll have a hard time buying it new though.
The remake is really love it or hate it--I liked the directors cut, and I don't really see how running reanimated corpses is any more or less plausible than the typical reanimated corpse, but a lot of people take this issue seriously for some reason.
I remember seeing a movie called The Cave that was similar to Sanctum, but I think The Descent take the cake for cave and/or cave creatures movies.
Definitely second The Descent. Just make sure not to get the US cut. Sure, the original ending is depressing as ****, but it's much better than a cheap jump scare that doesn't fit the movie's plot.