It all depends on the location I'm in during the fire, and where the fire originated. All things considered, in my house, it's likeliest to start due to a screw-up in the kitchen or someone dropping a candle.
Let's just go with me being in my room, since that's where I am nearly 24/7, and someone messing up in the kitchen. Since I'm in my room, and everything that's worth anything to me resides in my room, I would probably take as much as I could probably carry. I have a backpack here, so I could fill it with my 3DS and all the video games, my mp3, some books, and maybe a few of my favorite shirts/hoodies. The real issue is escape; I'm on the second floor, and assuming the fire and smoke has already covered most of the first floor, my only option is to jump down a floor onto the first floor balcony, and then jump over the balcony once more to reach the backyard. From there I can just run around the house and I'm safe. But that is assuming I don't break too many bones in the fall.
Well, to make things easier, I can use pillows from my bed to cushion the fall. But that's pretty much all I can do; I don't have a rope in here or anything strong enough to create a makeshift rope with. As for my computer, I would save it if I could, but odds are it wouldn't survive a fall from the window. .-.