They are at their absolute worst in the original PlayStation version, where they have no hitbox when leaping through the air so they can't be shot out of their primary attack. And they can poison you in parts of Code Veronica. Much deadlier than the literal spiders of the series. They're fast, jump at you from across the room, sometimes team up on you (in which case the fight can spiral out of your control with frightening speed), and have their notorious Deadly Lunge attack that instakills by decapitation.
Most famous are probably the Hunter class B.O.Ws, various ititerations of which appear throughout the series, being absent only in Resident Evil 2, Resident Evil 4, Resident Evil 5, Resident Evil 6 and Resident Evil 7: Biohazard, the last four being when the series dropped Big Bad Umbrella from the games.It's a tradition for the Resident Evil series to have these, particularly later in each game.