Giant Spiders made their first appearance in Castlevania II: Simon's Quest. In that game, they were pretty much portrayed the way they would appear in most following titles, by hanging upside-down from web threads and shooting projectiles, either cobwebs or their own offspring at the player.
In Castlevania II: Belmont's Revenge, they actually have a secondary purpose other than just being enemies; the player can use the web strings they leave behind to climb on and cross over bottomless pits. This adds a bit of strategy on how a Spider should be dealt with, as if it's killed when it's near the ceiling, it won't leave enough thread for the player to climb on.
As the series progressed, Giant Spiders were given a few different portrayals and ways of attacking, sometimes seen crawling on the floor at great speed, or attacking in clusters in an attempt to overwhelm the player.
First appearance of Giant Spiders in the series. These enemies are first encountered in Denis Woods, right outside the cave that holds the Sacred Flame. They crawl from side to side among the treetops and every given time they descend hanging from a web thread, shooting webbings at Simon. Due to them usually being out of reach and able of shooting projectiles at an angle, they may pose a threat if allowed to gang up on the player.
Giant Spiders in Dracula's Curse attack somewhat similar to their Simon's Quest counterparts, albeit now they appear in infinite numbers and they neither are visible from the beginning, nor do they crawl from side to side at the top of the screen. They lower themselves, hanging from a web thread from offscreen at the top on determined locations and attack; if not killed, they will simply climb back up and exit the screen. Another difference is that they now shoot little offspring at the player instead of webbings.
In Belmont's Revenge, Spiders, as usual, are found hanging from web threads, this time always above bottomless pits. Once dead, they leave their threads behind which can then be used to get across the chasm. For this reason, it's advisable to let them descend first and kill them when they are at the lowest point possible, thus leaving more thread for the player to hang on.
Pretty much the same variant from Dracula's Curse, although with Simon's ability to attack upward in any direction in this game, these enemies practically pose no threat, often allowing the player to kill both the Giant Spider and its offspring in a single whip strike.
Only a couple of them are encountered in the forest section of Stage II, and a couple more appear much later in the dungeons of Stage VIII, making this installment one of these enemies' less relevant appearances.
Unlike most incarnations, Spiders in Legends are found crawling on floors instead of hanging from web threads. They are the main enemies encountered in the Top Floor of the Castle (Stage 4). They move fast but only advance a few steps and then stop, giving a chance to kill them before they reach the player.
Spiders in Legacy of Darkness only appear as part of Queen Algenie's boss fight at the end of the Tunnel, beyond an alternate exit accessed through a sun door (granted the player arrives at daytime or holds a Sun Card in order to accelerate time).
The boss will be constantly giving birth to a myriad of these critters from the large egg sack she is attached to throughout the first phase of the encounter. They will be sent flying hanging from thin web threads all around the player in an attempt to overwhelm them, or at least hinder their movement so the boss can attack at will.
Physically, they don't pose much of a threat, as they can be killed with just one hit from any weapon. They will often leave behind Cure ampoules, which may become especially useful during this boss fight in order to counteract the Queen's many poisoning attacks.
Once the Queen has detached from the egg sack, she will no longer be able to summon any more spiders and will then resort in using her own webbings and melee attacks until the fight ends.