You begin Dragon Age: Origins by customizing your character and picking your storyline. You can be a man or a woman; you can be a human, elf, or a dwarf; you can be a warrior, mage, or rogue; and depending on which options you chose, you can pick where your character's home is (such as in the city or in the forest). You can also customize your character's appearance.
I've only played one beginning so far (Circle of Magi), watched one beginning (City Elf), and heard about one other (Human Noble). From the half I know, each one is different and will give you background information on that place. For example, because I started as a mage, I learned about the Fade before a dwarf, a human, or an elf in the city or in the forest would know much about it. I learned about the tensions between people in the Tower, so when I later revisited the place, I knew why it was in chaos.
The origin stories aren't very long, and my only complaint is that there isn't much of an impact on the overall plot regarding which background you choose.
Regardless of which origin you choose, you will be enlisted by the Grey Wardens, a group of powerful warriors whose job is warding off the darkspawn and protecting their world from the Blight. It is here you will meet Duncan and Alistair, and you'll be with dorky, special snowflake Alistair for the rest of the game as he tries to deal with his feelings for Duncan.
Just look at Alistair yearning for Duncan.
You can have up to three others in your party at a time, and you will recruit many others to choose from, including a war dog. The majority of the characters are pretty interesting. It's hard to learn about some of them because some are closed off and don't like to talk about themselves. (Sten kept hating me for asking him about his people.)
You can also choose your own dialogue options. With high cunning and willpower, you can shape others into doing what you want. You can also straight up choose to kill people. You can be an asshole or you can be a mild-mannered Grey Warden. Play the race or sex card, make people uncomfortable when you're a mage--it's all up to you. That freedom is what makes the game so enjoyable.
You'll fight dragons, go through some crazy dungeons (and in the Circle of Magi, a dungeon within a dungeon: DUNGEONCEPTION!), settle political disputes, travel to each unique city in Ferelden, and make your teammates fall in love with you if you so desire.
The one glaring problem with Dragon Age is a glitch near the end of the game at Redwall Castle. If you're not standing in a certain place, an ogre will never come to fight you, and you can't get inside the castle until you've killed that ogre. And you can't continue the story if you can't get inside.
The game is on the PS3 and Xbox and PC. It also came out in 2009, so if you're late to the game like I am, you should be able to find a used copy for around $20. The sequel came out in March and was listed as one of the biggest disappointments in gaming of 2011. I haven't quite decided whether I want to pick it up, but I may check it out if I can find it for a good price to at least see why so many people were upset with DA2.