Anyone who has used a welder knows that large amounts of sparks fly everywhere. They can easily ignite clothing (c'mon, who hasn't had a shirt sleeve or pants cuff start smoldering?) and flammable objects on the floor. Little molten beads of metal bounce all over the place and can easily go unnoticed while one's face is being shielded by the welding goggles or mask.
We do two things to minimize the chance of a fire. First, we wear old military shirts or jump suits made of Nomex, a fire-retardant material. The clothing has hundreds of little burn marks to prove how useful it has been over the years, by the way, and can be bought at any surplus store or over the internet.
Second, we've long since gotten into a little "ritual" when leaving the garage after welding. Once we've closed the door we turn off the lights and walk around the inside looking for signs of smoldering paper or cloth. It's amazing how easy it is to see the glow of a smoldering item when the lights are off. Have we ever seen something burning, you ask? Yes, several times over the years we've found a shred of paper, plastic or cloth on the floor. The fire might never have spread anyway, but who wants to take the risk?
Of course, we keep fire extinguishers in several places around the garage in case of disaster. There's also a phone extension in the garage. You never know...