There are a number of guilds in various places around Skyrim that your party can eventually join and ultimately even become guildmaster of that guild.  Not all guilds are for all players, however.  The major ones are listed below:

Bard's College (They're, well, bards.  Based in Solitude)
Companions, The (Noble warriors dedicated to combat mastery.  Based in Whiterun)
College of Winterhold (Mage's guild.  Based in Winterhold)
Dark Brotherhood (Assassin's guild.  You don't find them, they find you)
Imperial Legion (First of two main factions involved in the civil war.  HQ in Solitude)
Stormcloaks (Second of two main factions involved in the civil war.  HQ in Windhelm)
Thieves Guild (Membership has its privileges.  Based in Riften)

And of course there are other groups that you might be able to join once you've discovered them in-game.