A while ago I wrote an article about how to interpret public YouTube statistics. It appears that in the last week or so that YouTube disabled this feature on their video pages. Videos now just have an enlarged view counter with no interactive features.
At first glance it seems that the statistics have been taken off completely. However, upon further inspection, they have actually just moved the statistics to the left hand side next to the Like/Don't Like buttons as seen below.
Don't worry! Your video statistics are still available and so are the public stats on videos where the user hasn't disabled them. YouTube just wants to keep you on your toes.
All the analysis recommendations in the old post on interpreting YouTube statistics still applies.