If you are asking, are there spiders in Oblivion, you will not find normal wild spiders crawling around Cyrodiil. You will run into Spider Daedra, a spider-like Daedra enemy that shows up at higher levels and can be a nasty surprise if you are not ready for them.
In The Elder Scrolls IV: Oblivion, Daedric enemies provide the spider threat, not ordinary forest spiders. Their danger rises once you start opening oblivion gates and exploring the planes of Oblivion.

The Short Answer: What Spider Enemies Exist

You will not meet regular land spiders in the base game. The spider-like enemies are tied to Daedra, especially the Spider Daedra.
No Regular Spiders
Oblivion does not use standard giant spiders the way some other fantasy games do. You will not find cave spiders or forest spiders in normal gameplay.
Only Spider Daedra
The main spider enemy is the Spider Daedra, also called Perthan. According to the Spider Daedra entry, they are one of the tougher Daedra types and start appearing at higher levels.
Spiderlings Also Appear In Combat
Spider Daedra can summon spiderlings during combat when they are permanently bound. These smaller enemies can paralyze you. If the main Spider Daedra dies, the spiderlings disappear too.
Whether The Remaster Adds More Spider Types
For Oblivion Remastered and the Oblivion Remaster, the known enemy set still centers on Spider Daedra. Player reports around the remaster point to the same basic enemy type, not a new family of arachnid monsters.
Where You Find Them And When They Start Appearing

Spider Daedra appear in Daedric spaces, not the woods of Cyrodiil. Once your level climbs, you will encounter them as part of high-threat Daedra encounters.
Oblivion Gates And The Planes Of Oblivion
You will most often find them inside Oblivion or near oblivion gates, where daedra serve Mehrunes Dagon and the invasion is strongest. They can also appear in other Daedric-heavy areas.
Typical Level Range For Encounters
Spider Daedra begin appearing around level 17, according to the Spider Daedra reference. A separate UESP note on Daedra Venin says they do not appear below level 16 and are easier to find at higher levels in certain spawn areas.
How Often Most Players Will See Them
If you stay low level, you may never see one in a normal playthrough. Once you spend more time in oblivion gates and late-game Daedric zones, they show up often enough to become familiar threats.
How Dangerous They Are In Actual Gameplay

Spider Daedra are not just creepy-looking, they hit hard and move fast. Their mix of ranged magic, melee pressure, and status effects makes them more dangerous than many early Daedra.
Shock Attacks
They use a shock-based spell as their main attack and can also use poison spit. Your resistances matter a lot, especially if you rely on magic.
Speed, And Melee Pressure
They move very fast and stay agile in open ground, so kiting them is not always easy. If a storm atronach, scamp, or daedroth is also in the fight, the whole encounter can get messy fast.
Summon Spiderlings And Paralysis Risk
Bound Spider Daedra summon spiderlings, and those little attackers can paralyze you. A single stun can let the whole fight snowball.
Loot, Weaknesses, And Easy Counters
They always drop daedra silk and daedra venin, which makes them useful to farm. They are weak to frost and shock, so strong elemental damage helps. A tough summon or ranged setup can keep them from closing in.
Lore And Series Context

Spider Daedra have a clear place in Elder Scrolls lore. Their design connects them to a Daedric Prince, and they have appeared in more than one game.
Their Link To Mephala And The Name Perthan
Spider Daedra serve Mephala, and their alternate name, Perthan, comes up in lore and game references. That link explains why they feel more like a twisted Daedric form than a normal beast.
How They Fit Among Other Daedra
They sit high in the Daedra hierarchy and act as one of the tougher types you can face in Oblivion. Their combination of speed, magic, and summoning makes them stand apart from easier enemies like a scamp.
Appearances Beyond Oblivion
Spider Daedra appear in Battlespire and Legends. The Spider Daedra page lists several Elder Scrolls titles that include them.