The “Digg Effect” has been something of legends among some web development communities. It’s been known to crash websites, and this is what the term actually specifically refers to usually.
Speaking first hand (as of approximately a month ago at the time of this post) I can say with certainty now that a website on shared hosting, and the wp-supercache plugin installed for wordpress (which I mentioned in my top plugins for wordpress post) can survive it. I was very pleased with how wordpress held up under the stress in this arrangement.
Actual Traffic Screenshot (from Google Analytics)

As can be seen in the image just two days before the website had 0 visits, and then shortly after an initial surge which ended up totaling about 34,000 visits over the stretch! Pretty good! Not so impressive is the attention span of the average visit — the traffic only stayed for an average of fourteen seconds. Not very long. What is notable, however, is the traffic does continue for a long number of days after that having a steady slow stream which is far better than baseline was with the very last day totalling about 34 unique visits. This probably had much to do with the enormous number of facebook shares, reblogs, etc., and a general slight SEO/boost in the search engines, which I briefly mentioned in my backlinking tips post.
Viral Side Effects from Digg
This was some of my favorite parts of the traffic. Many of these visits were strictly side effects from people viewing the site from Digg, then immediately sharing it on facebook or twitter. This was made particularly easy for them by intelligent placement of share buttons.

Interesting to note that while Reddit was responsible for more than 20% of the traffic, pulling in over 7,000 visits, you can see the actual vote count on the post from Reddit is relatively low at 33 upvotes. The amount of traffic Reddit delivers is very specific to the actual subreddit submitted to (in this case reddit.com/r/pics). Having seen the amount of traffic just 33 votes can get you on Reddit, if you use a little imagination you might be able to come up with your own numbers on what kind of traffic infographics that get several hundred votes get.
The only two sites that did not pull in a lot of traffic was StumbleUpon and Google Buzz. StumbleUpon is notorious for being unpredictable and in some circumstances dumping far more traffic than even Digg and all of the others.