Companies that don't require resumes
squidoo.com
squidoo.com
If you are a superstar, have saved the whales from extinction, created an entire family of programming languages, invented self-replicating nanorobots or something similar you don't need a CV. Potential employers will look at the name and think "we've got to have that guy - no matter what" And your biggest problem will probably be to stave off the hordes of headhunters.
Unfortunately I don't fall into the above category, and I think that if I send an application to a potential employer that basically says "I couldn't be bothered to put together a resume so I just provided a few links for you to see how cool I am" my chances of getting the job don't exactly increase.
Besides many employers, especially large companies, have procedures they follow. For instance sending a CV around to a group of people you will potentially be working with, storing your CV in their internal database in case they have another job where you fit better, etc. Links to stuff you have done just doesn't comply to the procedure that many companies follow.
Any company looking for funding will also need to demonstrate its value/potential to investors. Part of this is demonstrating/documenting team competence.
Not a superstar badass? Starve. OK? Starve, Web 2.0 style. God we are so AWESOME.
"Formal resumes unnecessary (but they won't hurt, either)" http://friendfeed.com/about/jobs
I'm sure there are a lot that I'm missing though, so hopefully others can provide more examples.
(The lens also has a short essay I wrote about the value of a college degree for finding a job.)