Ask HN: Avoiding the “Hug of Death”

From time to time I see sites go down due to an influx of traffic from HN or Reddit. There are plenty of great solutions for serving static and dynamic content already out there so my question is, how come some sites still go down due to a traffic increase?

I realize that not every site will use nginx, varnish, or something similar. There are also many CDN services that offer a free tier. What setup would you use to ensure your site can survive a popular post?