At bare minimum there's a mod called Mo'Creatures that comes with an ingame config interface that lets you enable or disable any vanilla or Mo'Creatures mob (but not those added by other mods).
However Mo'Creatures heavily changes the way creatures spawn and despawn, and is known for significantly screwing up the play experience in many cases. Passive creatures, even those added by Mo'Creatures itself, more or less instantly die upon spawning because the mod also adds predator animals, and even one of those can kill 20-30 passives a day with ease. Combined with the fact that these spawns overwrite other mob spawns, it's very common to run into a situation where you can't find for example squid or sheep at all, ever. And let's not get into the numerous hostile mobs that will completely wreck all your building attempts just because they displace or destroy blocks around them by merely existing.
Maybe there are similar mods out there that allow for similar configuration without the hassle, but if all else fails you can try Mo'Creatures and disabling everything other than vanilla mobs (minus spiders).
However that won't affect the small poison spiders you find in mineshafts and under some Thaumcraft trees, because those come exclusively from spawner blocks.