Ding ding ding, we have a winner. KeepAlive can even kill your blog at 2 (achievement unlocked 4 times over last year).
Edit to elaborate:
Sorry, was eating dinner and Kindle is not exactly made for typing on technical documentation. This comment is a abbreviated version of http://www.kalzumeus.com/2010/06/19/running-apache-on-a-memo... -- read that if you want a longer spiel. (It is my most cited blog post on HN. I don't know whether to be happy or sad about that.)
Basically, there are a couple of Apache MPMs available. You may have the prefork MPM installed. You can check by running "apache2 -l". If you see prefork in the output, take a look at your config file (quite possibly /etc/apache2/apache2.conf) and check for the setting" KeepAlive On". If KeepAlive is on, your blog is broken and you just haven't found the failure condition yet.
On my server (Ubuntu, has gone from Dapper to Lucid over the years), the package default Apache2 settings for the prefork MPM are: 15 second keepalive, 150 MaxClients. If your server has enough RAM to support 150 processes for Apache (and, if you're on a VPS, you probably don't), that will let you process a hard theoretical maximum of 600 clients per minute. There are many, many things you can do to exceed that maximum bound: getting on the front page of Reddit or getting retweeted by Jimmy Wales at the right hour of the day both qualify.
Calculation: any client requesting any file, regardless of whether it is dynamic, static, cached, generated by a PHP monstrosity, whatever, occupies one process for a hard minimum of 15 seconds. 4 clients saturate one process for 1 minute.
With special attention to fellow VPS owners: after having died hard several times when apache2 decided to use up all available RAM and then swap the machine to death, I eventually tweaked the MaxClients setting down to 24. This means that, even with KeepAlive at 2 seconds, my max throughput was 720 clients per minute. Again, that number is achievable under very plausible circumstances for a personal blog in 2010/2011.
There are a variety of countermeasures one can take against this. One is not using the prefork MPM, but you have to be a configuration Jedi to figure out how to actually do this and still run PHP on your server. "apt-get install apache2 libapache-mod-php5", which is what substantially all guides will tell you to do, will force you to use the preform MPM. If you had been using the worker MPM instead, you would have a much, much harder time crashing your server serving static content.
Another alternative: switch to Nginx. This problem goes away instantly. (If I didn't have 15 config files I would have to migrate, I would have done this years ago.)
The easiest alternative: turn off KeepAlive. This will give you a very modest throughput hit, but I'll trade "Blog stays up if mentioned in the NYT" for that hit any day of the week.