So, factions in Oblivion, eh?
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In the game, there are four different factions in the land you can join: the Fighters' guild, Mages' guild, Thieves' guild, and Assassins' guild (the Dark Brotherhood). It's worth it to look at the previous game, Morrowind, in discussing these groups.
If you played Morrowind, you're probably thinking that that list is a little stingy. If you didn't, Morrowing had quite a few more guilds. On top of the above (although with a different Assassins' guild), they had three Great Houses you could join, two different religious organizations, and three different vampire clans you could align with. Most of these were mutually exclusive, but the replay value really holds up.
Where was I? Oh, yes. So Oblivion pared down the factions. A few other things changed. As a plus, the factions no longer require any sort of skill level. In Morrowind, you had to reach certain proficiencies with skills before you could advance in each guild. This meant that, for example, you had to get to a higher level before you could reach the highest tier of the mages guild. In Oblivion, you can play through to the end of each guild from the start of the game. Of course, the downside to this is that anyone can join any of the factions. Does it make sense to you that a fighter with no magic skills can become head of the Mages' guild? Or that a clumsy wizard who couldn't sneak past Helen Keller could lead the Thieves' guild?
Side note: Yes, Virginia, you can become a vampire in these games. Oblivion really didn't do enough with this, I thought. There are no vampire factions to join. The only related quest is to remove your vampirism. In game, you become more "vampire-like" if you don't feed; you get stronger powers, but your appearance changes and you start taking damage from the sun. This would be fine if the game actually reacted to your appearance change. Nobody cares that you're suddenly a monster. What a wasted opportunity.
The questlines involving these groups are very good. Many people seem to prefer them to the main quest of the game. The Fighters deal with a rival guild (which you can't join). The Mages try to stamp out necromancy. The Thieves . . . steal stuff. The Assassins . . . kill people. I realize those last two don't sound all that amazing, but playing through them will give you a good sense of how epic each one is. They're often quite a refreshing change from the non-faction quests, which tend to be of the, "Retrieve item X, then kill person Y," sort.
Overall, the factions are one of the great parts of the game. They'll take you all across the game world and offer lucrative rewards. What's not to like?