Blogs with no post dates are cowards
There... I said it... and I am just saying what everyone else is thinking.
It drives me nuts when I get a search result linking to a blog post about only to find it has no date. It is not that the date matters all the time, but when it does matter, its absence puts the entire post in doubt. If your blog is about song lyrics from the '60s you are probably OK with no dates - but what would hiding them gain you?
Most of the discussion about this I found on the Web is centered around the SEO value of using or not using a date on a blog post. Trust that Google knows how old the content is - you are not going to game Google on this. Instead, think about the reader. If I am searching for some technical information, and you are kind enough to blog about it, the date may be every bit as important as the information in the post. A five year old post about WordPress widgets will be pretty much useless. I need the date in order to evaluate the relevance of the content. Even the value of political discussions will change over time.
To me, not showing a date on a blog post is a sign that you are afraid of something. Maybe looking too old? Get over it.
As the Web ages, this will become more important. Hundreds of thousands of orphaned blogs will still be out there presenting information that may or may not be valuable in the years ahead. I say let the reader make that decision with the help of the publish date.