Isn't the title interesting enough ? Restoring your blog with having no latest back up? Yes ! It is not possible in a very good manner but still something is better than nothing. So let me get staright here to tell you this is an experimental way. It may work for some and may not work for others. All I want to do is to help those who are stuck in the middle of no where.
What I am assuming here is that you take back ups on monthly or weekly basis or atleast you do have a backup that was taken two months before your server HDD crashed.
Your blog is being cached by Google.
Your blog is at WordPress
If you have your old backup put it online and now you will be faced by a problem. You don't have any posts after that backup saved in. Now what to do. What you can do is to open that post in Google's Cache and copy the content post it again with the same URL otherwise use the article :How to republish your posts with a different date in WordPress?
How to open your articles in Google cache?
Well this is quite an easy thing to do. Just put cache before your url and see the magic.
e.g. Your url was http://domain.com/post123 you have to open cache:http://domain.com/post123 . Then copy its content and republish it.
What if you want to have a precautionary measure?
If your server is not crashed yet (Hope so it never crashes) then you can install a WordPress plugin that helps you in saving your data in a very unique way. One may ask how ! To answer this how let's see what is the plugin and what it is capable of !