Are you allowed to join multiple guilds in one play-through for your character? For some reason I keep thinking I heard that you can't. I just need some clarification.

Yes, you can. You obviously won't be able to join both the Stormcloaks and Imperial Legion, but everything else is joinable at once.

What you probably keep hearing is that people don't want to be able to join multiple guild at once. Some people think that it wouldn't be realistic to join the Thieves' Guild and the Dark Brotherhood, forexmple. Although I'm sure you will be able to join them all at once.