I had a cut to my left index finger due to a close encounter between it and the blade moving away from my face. I was a bit rushed and lost my focus.
Always pay attention and respect the blade. And never rush it - if you aren't proficient yet and don't have time to shave with the straight, use a safety razor. My worst nick occured when shaving in a rush. The result? Well... a stained white collar on a shirt.
The thing is: when shaving with the straight, you feel the edge on your skin and you feel the pressure your're putting on it. If the blade, for any given reason, sinks into your skin, it will only sink a very minor distance because you will feel it immediately and react by instinctively pulling away.
If you keep your cool and pay attention, you'll be just fine.
Just remember to never use a slicing motion.