I find these hyperboles amazing. I have a large number (currently 256) applications in my Applications folder and when I upgraded form 10.3 to 10.4 I found only 1 that didn't work - Retrospect client which is a dog of a program in any case (don't try to shift computers from user to user with Restrospect unless you use their uninstaller to find all the stuff it leave lying around your disk - for not real good reason). We're there a few changes in behaviour that might need a patch, sure, but these were no worse than what you get with any application (not OS). So if you'd like to back up broad stroke statements with some (a lot of) examples it might be nice.
Well, actually quite a lot of programs had trouble with OS 10.4 when it came out.
A quick check reveals one of the compatibility lists that still remains up:
http://www.macintouch.com/tigerreview/incompatibility.html
And, at the time, I was quite active in Apple's Discussion group, and found that I was constantly helping others with programs that no-longer worked for them. Usually, their only choice was to purchase a new version, or go back to OS 10.3.
It's quite honestly not worth my time to comb back through the archives to locate all those old discussions.
But, for myself, I do remember not being able to continue using any of the Symantec programs I had just recently purchased for OS 10.3. All those required me to purchase newer versions to enable full compatibility with OS 10.4. Those included their Internet Security and Anti-Virus programs, and their Norton Utility packages.
To this day, I still cannot use my Lexmark all-in-one with OS 10.4 as anything more than a scanner. Although Lexmark claims it works, it does not. It can be tricked into working if you use a backdoor method of configuring and printing to it through OS 9 in Classic Mode that a few of us stumbled onto. You have to set it up in Classic, then once you have it configured, aligned, and ready to work, then it may print from OS X 10.4. But, for the most part, the update to 10.4 turned it into a dedicated scanner. I don't even try to print to it anymore. Replacing the ink cartridges, aligning the heads, and getting it working requires either going back to OS 10.3.9 or using Classic mode.
I also found that Virtual PC failed to work properly or reliably anymore. But, Microsoft did release a patch eventually that fixed most of those problems.
I had several utilities from Intech (SpeedTools, and other maintenance tools) that became absolutely useless when I upgraded to Tiger. I didn't qualify for the free updates because I had purchased it at a discount from the company who sold me the drive - OEM version). But, they were happy to sell me a new license for the updated versions if I desired.
The older versions of TechTools failed to work, and required obtaining a new version. But, this was due to Apple having made changes to the file system.
I seem to recall some problems with Quicken not working properly anymore (but we later got a new version anyway).
I had a couple of hard drive backup tools that I was using which no longer worked (can't remember which ones). But, I know one of them was from Dantz (mine was an OEM version that came with my drive, so I wasn't eligible for a free update). Fortunately, I found a free alternative that worked fine.
Then there's Quickbooks (although they have since released a new version that can be purchased and will work).
I have some photo retouching programs that came with my camera that also doesn't work in OS 10.4. But, I've just moved all my photo editing to the PC. I have some nice tools on the PC that are more powerful. Sure, I have iPhoto on the Mac. But, for various reason I use it only as a place to store finished photos. I just haven't found it to be of much use for photo editing. I did try doing some red-eye reduction in iPhoto the other day, but it had trouble with some photos. On some, I found that no matter how many times I tried, it would put a black dot on the subject's teeth instead of the pupil of the eye. On others it worked fine. Over-all, it's just too much trouble with iPhoto. So, the PC gets that job and other photo retouching jobs.
And, of course there are a ton more that quit working as well. But, fortunately, free programs have free updates. So, that wasn't much of an issue.
There were also a small hand full of lesser established video editing programs that I was using that were no-longer useful. Can't remember all the names now as it's been a long time since I messed with them. Once they quit working, I quit thinking about them.
And, there were others that I just cannot remember at the moment. I dumped (sold) all my old programs that no-longer worked with Tiger when I sold one of my other computers that had OS 10.3.9 installed on it (basically threw them in as a bonus for the person who purchased the system). If I still had them all here, I'd happily run through the list of titles that I had. But, time has passed, and I haven't spent much time dwelling on it.
So, the items above are just the ones I can remember right at the moment.
As for others, I do recall helping a lot of people who couldn't get Virex to work anymore.
And, I also recall helping a lot of people who's device drivers wouldn't work. So, if the manufacturer didn't release updated driver, then they had to buy a new device to replace that item.
In the end, the degree to which compatibility affects you will be determined by which specific programs you use. If you happen to use programs that offered free updates, then you'll be less affected. If you use programs who's authors decided it was a good excuse to charge for an update, then you'll be affected more significantly.