People who only read NYT stories when they encounter a third-party link will never see the paywall, while someone who actively uses the NYT as a regular news source eventually will.
Everytime I've hit the paywall, all I had to do was delete my cookies and history. I could then reload the same URL (from the same ip address) and get back in for free.
But after a couple months of doing this, I paid for access. I'm not a rich man, I don't have money to throw at things I don't need, but I felt that the value I was getting from the NYT's reporting was worth paying for. I can't buy a copy here (although I do when I'm in the US) so this is my way of supporting great journalism.
I wonder how many people like me are out there - circumventing the paywall with ease, reading as many NYT articles each month as they want for free, but eventually deciding to pay to support the paper? Or am I an edge case? What I'm getting at is maybe the paywall's deliberately easy to get around, so you realise what value you're getting from the NYT.