Digg.com is a fantastic site, it has an amazing influence on making stuff popular. But, it is also a constant burden on website owners. If you get "dugged" you got to have a very good hosting plan in order to stay online.
I have been dugged about 5 times within the last 6 month or so. Most of the times has not been very spectacular with only a few amount of digs. But, 2 times the traffic increase so much and so fast that my website crashed.

1: The first time was in August, just after I had released WEB2DNA. Once that got on Digg.com the website was literally under siege. It crashed 4 times because of the high amount of traffic, and I eventually had to redesign how each DNA was made in order to handle the high traffic loads.
Eventually, my "15 minutes of fame" was over, and the traffic returned to its normal level.
2: The second time was two days ago, when an old article about the usability of package tracking appeared on the front page of Digg.com. As you can see, that created a amazing spike in traffic. In the morning (European time) I had between 2,000 - 4,000 visitors per hour. After the initial barrage things seemed to slow down, as most people in America went to bed.
But, they only slept for about 8 hours, and when they woke up they came back in force. The number of people coming in was so high that the server crashed and stayed down for about 2 hours. A few was lucky enough to get in, but it took ages to load the page - and the images would did not load.
Don't get me wrong, I like getting dugged - it is fun! But, my server does not seem to agree with my point of view.
There are a number of things you can do to prevent overloading the server.
And if none of these work, you need to look at your hosting solution.
You can also consider to simply ignore the problem. After all, getting dugged does not happen very often.
For my part, I have already made some reductions. I have found a new host (which did a much better job than the old one, but still could not handle it) and I have some other things I might change in the future.
Jesper Rønn-Jensen - Oct. 17, 2006
As Aleks pointed out, the HTTP headers can be really useful.
I know for a fact that Danish Broadcasting Corporation (dr.dk)'s servers have been downed by responding "not modified" to every browser request for static files like images and css.
At Yahoo!, for instance, they use another technique:
Setting expiration header for static files to a point in the far future. That means that if you (as a webmaster) want to change an image, you'll have to rename it.
Also, putting static files on a separate server prevents cookies from consuming bandwith (your site has 4 cookies).
The downsides are little compared to the upsides: More traffic with less bandwith consumption and less horsepower.
It would be relevant in particular to someone like you that writes such good content!
Blaise - Jan. 25, 2007
Reduce server handling is a good one. Certainly SQL queries can make a page very slow, so avoid them where possible.
For example: save a full copy of a page you're outputting. Refresh it when new comments arrive or when you adjust your weblog.
It's also possible to cache smaller parts of a page that constantly change. Just cache it on your server and update it every minute, 10 minutes or every X pageloads.
Caching (serverside AND clientside) is always good practise, not only when your website is dugged.
Published: Oct. 14, 2006 in Technology
Thomas Baekdal - Oct. 14, 2006
Ahh... just noticed. I was actually dugged twice within the past 36 hours, which better explains the explosion in traffic.
The other article was my car advertising tutorial.