Bethesda seems intent on reworking the number of factions available to you in each game. In Daggerfall, you had a dozen or so guilds that you could join (the Temples were later patched so that you could only join one); in Morrowind you had about ten (although there were three Great Houses, you could only join one); in Oblivion you only have five: the Fighters Guild, the Mages Guild, the Thieves Guild, the Dark Brotherhood and the Arena. The Temples appear to have also gone the way of the dodo. These factions are your bread and butter for quests. You gain some advantages just for belonging to them, you gain ranks and more benefits as complete their quests (no skill checks for guild advancement in Oblivion - not sure if this is a good thing or a bad thing), and you get some really nifty perks for reaching the top rank.
The Fighters Guild contracts out muscle to those with the money to pay for it. There are guild branches in just about every city, but quests are only available at the ones in Chorrol, Anvil and Cheydinhal (I suspect that some kind modder will recitify this shortfall). The requirements for joining are...uh...err...hmmm...well, you get the idea (requirements? we don' need no steenkin' requirements!). Anyone who thinks that they have a big case of bad-ass is welcome to join. The requirements for staying in are pretty standard: don't commit crimes against fellow members. If you should misstep, you can earn your way back into the good graces of the Guild by performing a pennance quest. The pennance quests are "simple" ingredient retrieval quests (20 bear pelts for your first offense and 20 Minotaur horns for your second), but bears are level 7 creatures and Minotaurs are level 12 creatures, so don't step on toes early in the game. It's a "three strikes and you're out" situation, so be careful.
The Mages Guild has a monopoly on magic in Cyrodiil (Restorative magic can be had from the Chapels as long as your Fame is higher than your Infamy), but in Oblivion they do not contract out their services (I see an opportunity for more modding). Their quests tend toward finding information or items for research or resolving internal political issues. The overarching story of the questline is the complete elimination of Necromancy in Cyrodiil, so expect to run into lots of undead and spell-slingers. It's the same rules as every other guild: don't commit crimes against members and there are also a couple of pennance quests for those who have to learn the hard way. The pennance quests are ingredient-retrieval quests. If it's a minor violation (stealing from a guild member, for example), you'll be scouring the land for some rare flowers. If it's a more serious infraction (killing a guild member), it's Daedra Hearts and Vampire Dust, which typically need to be collected from dead Dremora and dead Vampires. Dremora aren't that big of a deal since they're all over the place on the other side of Oblivion Gates (Main Quest). Vampires can be a bit trickier, but there are a few places where you can always find some. Memorial Cave is perhaps the closest (it's SE of the Imperial City) and has a few, as do a few abandoned forts (Fort Carmala, for instance) and Ayleid ruins (Lipsand Tarn, north of Chorrol). Clean 'em out, wait a few days for more to move in, clean 'em out again. Repeat until you have your 20. In both cases the ingredients can sometimes be purchased through Alchemist shops, but it will take a while to do it that way. Again, on the third offense, you're banned permanently.
The Thieves Guild is a bit more like it was in Daggerfall. It's an underground organization and they will contact you once you have done those things that indicate your interest in joining. Unlike the other guilds, the Thieves Guild has no pennance quests. Instead, you pay fines. So offend to your heart's content as long as you have the cash to pay for it. Unlike the other guilds, however, the Thieves Guild has a strict "no killing" rule. If you kill someone while stealing for the guild, you'll pay a 1,000 gold "bloodprice". In addition to having to complete quests for adancement within the guild, you'll also have to fence a certain amount of stolen merchandise for promotion to the next rank. The fencing requirements are rather modest, but I'm not factoring in the high Mercantile skill of the guild fences in making that statement, so your mileage may vary.
The Dark Brotherhood, an enemy faction in Morrowind and the Tribunal expansion, is back with a vengance in Oblivion. Like Daggerfall, it's an underground faction where you have to be invited to join. Like the other guilds, you can't commit crimes against your fellow members. But there are no pennance quests for infractions, at least not in the traditional sense. The Dark Brotherhood has a rather direct way of dealing with malefactors: you're visited by a Wraith and, if you survive, you can be readmitted. However, it's still a "three strikes and you're out" affair. Even if you defeat the wraith following the third offense, your career in the guild is finished.
The Arena is a different sort of experience. You don't join so much as you choose to participate. You can participate as a spectator or you can participate as a combatant (or both). Participating as a spectator boils down to making money by gambling. You bet on either the Yellow team or the Blue team and then collect your winnings (or eat your losses) after the match. Participating as a combatant comes down to defeating a long series of opponents in a long series of fights until you are the undisputed champion. There are no rules for membership, no quests, no puzzles. Just fight and win.