As someone with an IT/IS background...
There are a number of reasons to stay current. Some have already been mentioned while others not. There should generally be a "slight" delay and a check for compatibility issues unless the patch/update solves a critical problem or critical security flaw.
Reason 1: Security
Reason 2: Compatibility with customer demands
Just because you use common sense and wait a reasonable grace period does not mean customer or their agents X, Y and Z are not going to rocket forward.
Side-note: Whether it be true or not, do you people who demand "we only accept CS3 files" realize how terrible and backwards you look to the customer? If you are unable to accept files more than 1 version from the current version "YER DOIN' IT WRONG!"
Reason 3: Unsecured/unrestricted users making their own decision (Matt described this as user fanaticism, that's definitely sometimes the case)
Reason 4: Backwards compatibility nightmares.
Just in this narrow prepress view:
Yeah, your MacOS 10.2 computer has worked just great for half a millennia. Awesome! Good for you! But good luck making anything you've generated work when you upgrade and skip 10 versions of software. I've personally been through this nightmare over and over again with people still using PageMaker, ancient versions of Quark (or current versions for that matter), Ancient versions of other Adobe apps, Macromedia Apps, etc. Yeah... you're not going to be able to open those 10,000 Freehand documents with Illustrator CC, InDesign CC, etc. and No, we can't buy Adobe CS1 for you now.
From a budget perspective:
It's typically a whole lot easier to buy 4 of 5 computers with all associated software every year than it is to buy 50 every 5 years.
Reason 5: Forwards compatibility for support. As someone already mentioned vendors stop supporting legacy software for good reason.
Now for a rant:
These software vendors who like to lag behind 6 months to a year+ are a huge headache and problem. Clean up or restart your ancient code base, get organized and wake-up to 21st century development models. I'm not going to sign-off for the $25,000 a year service contract and continue buying your software if you don't shapeup. I'm not going to pity you for outsourcing all of your development to enrich yourself with a 30% margin instead of a 20% margin.
I've heard countless vendors support groups tell users "don't install windows updates on the X server!" and "you can't run antivirus and anti-malware software on server X". You've got to be #$#ing kidding me right? Do you want me to leave the doors unlocked and the security system disabled when I leave every night too?
Personal anecdotal story:
I have one critical server from a particular press vendor that literally breaks every time a windows update is installed. This vendor has made their equipment only accept presetting data from their proprietary software that this server runs. It runs only on Windows 2003 (zee parent company tells us nothing so no, vee don't know what zee upgrade schedule is). "We don't support virtualization why would you want to do that?". I call their support repeatedly "uh, yeah we uh, don't know what is causing this um.. hmm.. never seen this before". I finally figured out the problem myself and had to write a procedure of manually stopping/starting services.
Whew. Needed to get that off my chest!