What are some of the inventions discovered completey by accident?
Sillt Putty.
Seriously!
Vulcanized rubber. Goodyear was working on the process, but the combination that worked was pretty much accidental.
I meant “Silly Putty”.
the irony 
Cyanoacrylate adhesive (super/krazy glue) was the result of a failed experiment to produce either artificial spider silk or clear plastic lenses (sources differ on the detail).
This sort of thing would appear to be quite commonly true of invention and discovery, except that the stories of the original discoveries/inventions with which we are so familiar are often romanticised to some degree; for example, there is considerable controversy over the story of Fleming’s accidental discovery of penicillin.
Teflon. While attempting to make a CFC refrigerant it stuck to the inside of the container and nothing came out. They cut open the container and behold, they had teflon.
Viagra - developed as a treatment for (I think it was) high blood pressure (or something.) Turned out to have more interesting side effects.
The adhesive used on Post it Notes. Guy invented an adhesive that didn’t stick very well and went looking for an application to use it on.
Here is a good page about the troubles that were encountered trying to find a use for this stuff.
interesting…
he discovered a “process”
Actually, they’re just now starting to market it as such.
It is my understanding that the original process of developing sharp, long-lasting photographs was accidentally discovered by Louis Daguerre. Plates he placed in a particular cabinet developed very strong and dark images; he eventually figured out that the excellent developing was the result of mercury vapors present due to an earlier chemical spill in the same cabinet.
Newcomen’s original steam engine.
The first design attempted to use steam pressure to force up the piston. At the top of the stroke, the cylinder sprung a leak. The steam condensed, forming a vacuum, which pulled the piston violently into the cylinder, breaking the boiler.
Newcomen, impressed by the force developed, changed the design so that this happened on every stroke.
Wasn’t that kind of hard on the old boiler repairman?
I think Minoxidil (Rogaine) was also a blood pressure medication with an interesting side effect (hair growth in this case).
LSD. The telephone to an extent (Bell was working on a way to help the deaf when the application diverged).
There’s a whole book about this: “Serendipity: Accidental Discoveries in Science”. See http://www.amazon.com/exec/obidos/tg/detail/-/0471602035/102-1836977-7184132?v=glance
The ‘Slinky’.
Note that 3M likes a good PR story as well as anybody, but some key info that would indicate that it was far less than luck was left out. PBS had an invention show waaay back and they interviewed the inventors. They had an adhesive category that displayed a range of properties. They noticed that at one point on the curve, the adhesive might be strong enough to support paper but not too strong that it would tear paper when removed. Experiments proved it.
Serendipity had no more to do with it than any other advancement in Science.