Some of the most popular posts on my blog are from the distant past, and although they're still relevant, I'm concerned that people might see the post date published in the Goog results, and not bother to click because it's an old post. Is there any disadvantages in removing the date that posts were made?
Kerosene, There are a few disadvantages, especially if you have inbound links pointing directly to that post. If you decide to remove the dates and use a different permalink structure, you can always use a redirect. -BlastFree
You may find this plugin useful if you change your permalink structure. http://wordpress.org/extend/plugins/smart-404/
I think it might let your visitors go away when see the post date. But I'm not sure will Google remove the post date from the SERPs or not. I see some popular Wordpress sites don't use post date in their permalinks and even don't show to users.