Babies who slept in a room with a fan were 72% less likely to die from SIDS, according to a study released from Archives of Pediatrics & Adolescent Medicine. The study included interviews with the mothers of 185 infants who died from SIDS and the mothers of 312 other babies.
I have to say that my theory on why fans have this effect is slightly different from the conclusion that the study authors came to (who don't know exactly why fans seem to help, it's possible that fans improve air circulation, preventing infants from rebreathing exhaled carbon dioxide, which can pool up in the gap between a baby's face and the mattress). While I think that point is definitely valid, I doubt many (if any) of the kids in this study were placed on their tummy to sleep, which would be the only way for carbon dioxide to pool up in front of baby's face.
My theory is that air blowing lightly in the baby's face triggers their natural reflex to inhale. If you have a young baby, you can try this: blow gently in their face and they will take a quick, deep breath. This works great for example when your child hurts themselves and "screams silently" without breathing in. Our oldest would start turning blue and almost pass out until I learned this trick. Now I just give a quick blow in their face, which makes them stop screaming to take a breath.
This is another reason why I LOVE LOVE LOVE having my youngest baby always tucked in by my side to sleep at night. They do not need a fan because while I am sleeping, I am constantly breathing on them lightly, which is like a "breathing pacemaker" to them. I believe that this is a major reason why "co-sleeping" babies have so much lower rates of SIDS. Breathing is an involuntary reflex, but in some babies it is a still a little immature at birth and they simply "forget" to breathe. The natural reflex to breathe does not kick in, and they die. Of course, there are many contributing factors (such as cigarette smoke, not being breastfed, etc.), but I believe that these come into play only because they disadvantage the child and further undermine his/her health.
I am a firm believer that all young babies should sleep with their parents, and that parents need to take precautions to ensure their bed is baby-friendly (i.e. no gaps, guard rails for older babies, etc.). If you or your spouse are intoxicated, have taken prescription medicine, or are extremely obese, having baby in bed with you is NOT safe, as you may inadvertently roll over them in your sleep.
You can find lots of information on safe co-sleeping habits online or at the library.
Edited to add: Please check out this post on important information regarding the safety of (crib) mattresses.