Spoiler for rant I wrote a long time ago, that you don't want to read:
I clearly paid a damn fair bit for this thing, yet I'm forced to watch through a 30 second spiel about not pirating it, every single time I want to watch the DVD. It's just so unfortunate they can't get this message to the actual pirates though, only legit buyers see these things (scare campaign to stop legit users going into piracy?)...
Add to the above that stupid "would you 'borrow' a car?" ad (and to answer it, no, because I can't drive - makes stealing a car that much more difficult)
Disc is filled with CSS encryption, region locking, macrovision or whatever other protection schemes there are out there just to make it that much more annoying to whever buys the thing. Since when did these stop piracy?
Haven't seen this with DVDs, but the potential for something like the Sony BMG scandal may be lurking around... I guess pirated material may contain viruses too, but these are probably more evident than a hidden application which autostarts when you stick the DVD in the drive, also as you probably scrutinise the downloaded a bit more than a purchased DVD.
Discs are more difficult to back up, not just due to protection schemes, but also due to size. I guess this can partially be blamed for the fact that DVD uses MPEG-2, but a downloaded 700MB movie is somewhat easier and less costly to backup than a typical 4-8GB DVD.
On a similar note, if you want to stick your movies on that big 1TB HDD you bought, a number of DVDs will add up, chewing up more space, unless you take further effort to transcode it, which brings us to...
More difficult to transcode; for those downloaded AVIs, to put it on a portable player, most programs will just let you convert the thing straight off. DVDs are often a bit more complex, especially if you want to split stuff up by episode, for example.
Requires a DVD drive - although most computers have optical drives these days, systems like netbooks don't, and with the increased usage of the internet, and larger HDDs, it's probably only a while before the optical drive starts losing some popularity