When my boyfriend and I were living together, his parents bought him a safe to store all of his important documents in and I got to use it by default. The safe they bought him was by SentrySafe Fire-Safe and it was a cute little chest. It was bright blue in color which I liked, and fit perfectly under our bed. It required a key that we usually kept in the nightstand (yeah I know, not the best place but it worked for us) and it was very easy to open and re-lock once you were finished with it.
It was just a small chest so we kept mostly important documents like the titles to our vehicles, birth certificates, social security cards and extra cash we were saving up for bigger apartment purchases. We never had a fire, thankfully, so I can't really say how it does when faced with that but it's supposed to withstand up to 1550 degrees for a half hour. A half hour isn't really that much time, but hopefully if you do have a fire, it's put out within a half hour.
The chest had a very nice carrying handle and it was just under 15 pounds so it was very easy to transport from room to room if I needed to.
Now that my boyfriend and I no longer live together and he took the safe with him I have been thinking about purchasing a safe of my own. I have found some very similar looking safes at Office Depot and Office Max for around $40-$50. Not a bad price to pay to protect your important documents.