In Morrowind, the guilds didn't really have a storyline, but each guildhouse had a specific theme and associated quests. Let's take the Mages' Guild; Balmora's head had a dislike for the Telvanni and necromancers, as well as a hard-on for the Guild itself, which was reflected in her quests. Ald-Ruhn had a Dwemer theme in its quests and Sadrith Mora's theme was exotic scholarly knowledge. As you do the quests, you slowly find out that the current Archmage is something of a moron and you were set to take his place courtesy of Chancellor Ocato or your own initiative.
In Oblivion, you started off with making your way into the Arcane University, having obtained recommendations from each Guild Hall. Then, you make your way up the ranks; from Associate to getting your own Mages' Staff to Archmage, and the history of the guild slowly unfolds as you deal with the rumors of Mannimarco's return. The one time you're treated like a disposable grunt, you get an apology; all other quests from that point on show that you're a trusted member of the Mages' Guild and you get them because your bosses think you're badass enough to handle them. The culmination of the questline is the Archmage himself entrusting you with stewardship of the guild and destroying the King of Worms.
In Skyrim? You're a grunt. Full stop. You don't progress through the story, gaining the trust and confidence of your guildmates. You just get told what to do. You don't even find out a thing about the Eye of Magnus, other than it being a magical doohickey.

