Every search engine does fun and interesting things (try searching for do a barrel roll in Google), and DuckDuckGo has a few fun ones as well. Here's a list of some of the ones that I found particularly interesting.
days between 01/01/2000 /03/31/2014 tells you how many days there have been between the two dates (but remember to do it MM/DD/YYYY, rather than the proper, ie. British way!)
argos coupon tries to find any coupons that are available to save you money on stuff.
google+ philbradley will find you people with the searched name who are on the Google social network.
@philbradley will find you information on a Twitter account, as well as their last tweet.
password x strong will create a password for you that's a mixture of characters and symbols which is going to be difficult to break. Just replace the x with the number of characters that you want, obviously.
qr code bbc.co.uk creates a QR code for the requested website.
expand https://bit.ly/a will expand out the URL so you can check where you're going before you get there. (That one takes you to Apple.com in case you were interested)
is bbc.com up? will check the required site to see if it is currently available.
There are plenty of others, and I found these via a handy cheatsheet over at Techglimpse in case you're interested in looking at shortcuts that specifically relate to geeks, techies and system admin folks. For the rest of us though, this is probably all that you'll need!