[miaskows]

What do you think was the mostly unpredictable and random discovery in chemistry?
By my opinion it was synthesis of C6(OH)6 (hexa hydroxy benzene) by passing of CO above melted potassium:
6K + 6CO = C6(OK)6
C6(OK)6 + 6H+= C6(OH)6 + 6K+
Unbelivable, isn't it?
 

[jdurg]

I would have to say that Polytetrafluoroethylene (Teflon) is the most unpredictable and random discovery.  They just had a cylinder of fluorine gas with a special coating on the inside, and suddenly they saw that the pressure inside the tank was dropping but there was no F2 leaking out.  They eventually opened up the tank and saw a white substance lining the inside.  Teflon had been discovered by pure accident.

[movies]

As a synthetic organic chemist, I would go with Perkin's inadvertent discovery of mauveine (c. 1856) that ultimately led to the chemical dye industry.  He was attempting to make the natural product quinine (found in tonic water, by the way) by simply heating 2 equivalents of N-allyltoluidine in the presence of oxygen.  Today, this would be a laughable experiment since there is no chance that the sponataneous formation of quinine would occur.  Perkin found that the reaction produced a black solid.  At this point, any modern day chemist would probably give up, but Perkin attempted to extract this tar with a variety of solvents and found that when he extracted with alcohol he obtained a brilliant purple solution that was a potent dye for fabrics.

Perkin made a lot of money off of that discovery.

[Garneck]

Conducting polymers.

I don't remember who discovered them, but it was some japanese guy. He and his staff just wanted to polymerise acethylene but they added too much of the catalyst and they got a doped polymer that conducts electricity.

[Mitch]

A very cool polymer indeed. It looks just like metal.

[constant thinker]

The Teflon discorvery is funny. I would say the Teflon one is cool and funny. The scientists were probably mad for a second when their flourine dissapeared.

[Benzene265]

I like the discovery of cold stretching polymers myself.  The first thing the DuPont scientists did with their gloppy pile of nylon was see how far it could stretch down a long hallway.

I'm also a fan of Archimedes and his discovery of buoyancy.  Sure, it's not chemistry, but the story has a great mental image.

[AWK]

Most people like jeans trousers dyered by indigo. What about of indigo synthesis discovery by Fisher. Many student crystallize phenylhydrazone of pyruvic acid from alcohol under his supervising, but only one student produced deep blue insoluble substance. After prolonged examination Fisher realized that this student  kept alcohol in the bottle previously used for HCl, an indigo was formed as a result of pyruvic acid phenylhydrazone rearrangement under acidic conditions.

[movies]

indigo was formed as a result of pyruvic acid phenylhydrazone rearrangement under acidic conditions.

You mean a Fisher indole synthesis?!