What are some awesome things people can do while riding a bicycle?

Packing and smoking a pipe.

When first I visited the U.C. Davis campus, one of the first individuals I saw was pedaling along at a decent pace, playing a small, wooden flute of some sort (a transverse flute, not a recorder, but I doubt it had keys) He's probably still not "normal" exactly, but this guy (and you'll find a few others) plays a full-size piano and sings while biking. Regarding 's answer, if we're going to include unicycles and stunts, we'd better mention the likes of this unicyclist. She unicycles and dances at the same time.

Well, Steve Roberts' bikes [1] were far from normal, but he actually built chording keyboards into the handgrips so that he could type while biking.  He also had a ham radio installed, and in his last edition of his bike, a refrigerator that could circulate chilled water through his helmet. [1] http://microship.com/resources/winnebiko-behemoth.html

If bicycles and tricycles are allowed, I will also include a unicycle rider: He is (or was - I think he was mostly active during 60's and 70's) a bit of a local celebrity, and could besides the hula hoop also juggle or play the trumpet while riding. Then again it may run up against your request of "normal people"...

Answering my own question here, but someone on Facebook shared this photo and it's awesome:

While probably less high on the ooh ahh scale, this video about the burgeoning cargo bike movement has many people doing what in our society is a huge deal: Leaving their car behind. And having a hell of a time! (R)Evolutions per Minute: Cargo Bikes in the US - a trailer for the crowdsourced documentary  

You can move through many cities faster than any other form of transportation, even motorcycles!  In the US, this has to do with finding parking, as well as selective enforcement of traffic laws.  The small size and weight of a bike mean you can fit in smaller gaps (like stairways) and overcome bigger obstacles (like guard rails) than other vehicles.  I'd guess bicycles have a distance range of about 1 - 12 miles where they're fastest.  Above this, motors make you faster, and below it, running makes you faster.  Most people have no idea how fast it is possible to move through traffic on a bike:  http://www.digave.com/videos/#top

This is a great question :D I loved it so much that I posted the most awesome things you can do on your bike on my blog. I used some of the images posted here and updated it with some more... like a bike toiled, a beer bike... Check out: http://Bikestein.com