The spiders... and it gets worse. There's the Black Tiger. Technically, the Black Tiger is a huge tarantula in the first game, as are the other giant spiders. The remake bases its design on the Australian funnelweb, about a hundred times more deadly. Course, if you're an arachnophobe, this doesn't help at all.
The atmosphere of the games. Just about every game, but particularly those with the Sprite/Polygon Mix, will have several rooms that have no enemies whatsoever in them, and yet will make your skin crawl, via a combination of lighting, camera angles, environment details and the series's love of Hell Is That Noise with their soundtracks. Just which empty room is worst varies from player to player, but every game has at least one of them...
The T-Virus infected animals are even worse than most of the zombies.
Owing to the fact that the backstory of Umbrella is developed over several games in the series, this belongs here. Quite simply, the people that work at Umbrella are terrifying even before any infection or transformation. Take their top researchers, Wesker and Birkin. Birkin is one of the series' most frightening creatures after his transformation, but he and Wesker were monsters far before their respective infections. Just look at how they developed their viruses, particularly their treatment of Lisa Trevor. Callously and without any concern or remorse, they experimented on her and others for years, and casually discarded her once they had the prototype for the G-Virus. Despite this, Birkin later had a family, including a daughter not much younger than Lisa was at the beginning of her experimentation. It was originally Spencer and Marcus who had her (and her mother) used as a specimen; the lack of humanity in the Umbrella higher-ups is quite frightening in its own right (especially since such human experimentation apparently free of ethics has happened in real life).
The music. Probably unnerving for some first time players, but it still messes with you. Especially if music randomly plays (i.e. Resident Evil 4) and you're just wondering what the hell is to come... And in some moments, they're just screwing with you.
Save rooms. They're known as places of safety, down to the music they play. Resident Evil 4 uses music alone to mark safe zones. Consequently, the few places where they break safe zones are absolutely terrifying.
Windows. Yes, windows. It's almost a Running Gag in the Resident Evil series. Ever since the first time you run into Cerberus in Resident Evil 1, you eye every window with suspicion. Any pane of glass in the Resident Evil series may have some unknown horror behind it. It's especially ominous when you see the zombies banging on them, attempting to break in. More often than not, any window you see is likely a Chekhov's Window. Something at some point in time will leap through it and try to kill you.
The Game Over screens are almost as scary as the games themselves. The later games less so, probably due to the letters being a regular font as opposed to the bloody, red letters they used for older games. Older games usually included the killed character either being killed or dead, while Code Veronica just had the character scream'' as the letters "YOU DIED" melt away...