Honestly, I had 5 - I dropped out of school when I was 18 - that was ten years ago though. Yes, 10 years. I'm old. Anyway, I got in. They're not the end of the world, if you use my life as an example.
Correct me if I'm wrong, but according to the AMCAS manual, W's are neither assigned an AMCAS grade nor an AMCAS credit... i.e., you must list them on your app, but they're not factored into your AMCAS GPA.
If you have a couple not a big deal. I had two and they were never brought up. I'm sure if you had three every other semester there would be questions. If you have sound reasons, it shouldn't matter. Most importantly, a W is considerably better than an F or D. If you are doing that bad in a class your gpa will suffer and you would most likely take the course over again anyway.