Because I know 99% of you won't take the time to watch the 6:11 video, I'll paraphrase his argument. "Your DVD will end up in the trash because potential employers don't want to waste the time it takes to put your DVD in and watch it. Get a website, put it on your business card, and hand these out instead. Direct all of your traffic to your site."
While he makes two arguments that I agree with, I have to call foul on everything else.
1) I'll mirror my comment to his video here by saying I agree that you need a website, or at least a blog that showcases your thought processes, demo reel and other works. I'm sure a lot of larger studio's don't have the time to sit around and read someone's blog and their thoughts as to why they think Cubism is teh sexorz, but I think a lot of employers would like to get into the head of a potential hire.
2) I also agree that DVD's are a waste of money, time and resources. So is paper, but I don't see us getting rid of that any time soon.
When it boils down to it, the following is always true: Luck favors the prepared.
Case in point, I submitted soft copies of my demo reel, breakdowns, resume and cover letter to about a zillion studios. I found out later that one of those companies would also like a physical reel on DVD. Whoops. I didn't have one so I had to rush and make it (not that it takes that long, but still). There are a LOT of companies that still require a physical reel and just because there's a chance they'll throw it away without watching doesn't mean you shouldn't have one. Who cares what they do with it?! Your future is worth more than that $0.50 cent disc.
As a student, I think you should have an up-to-date reel online at all times. You should be working on something often enough so you're able to update and improve your reel once every three or four months. Put it on your blog, Vimeo, YouTube, pimp it out on CGTalk. It's all free and you open yourself up to great feedback. Don't be silly and make an obscene amount of DVD reels because whenever you update your reel, those remaining DVD's become useless. You should, however, have SOME copies of your reel on DVD (my modest range is 5-7) and hard copies of your resume, breakdowns, art work and what have you at the ready in case you are required to mail these things in, or you run into someone who wants them.
One thing I do promote having a good amount of are business cards, but be smart about it. Don't print off 10,000. Also, only put information on these cards that isn't likely to change in the near future.
E-mail address (firstname.lastname@example.org, nothing crazy like HotMama69SweetCheeks)
Make sure the back of the business card is of a light color and unmatted so the other person can jot down other information if they need/want to.