Yes. Bit errors are uncommon and range from benign to crash. Your storage has them, memory has them, network has them. Non error correcting memory very significantly increases risk. And this is the kind of risk you don't notice, until you do and when you do, it's often subtle, insidious, impossible to track down. Servers absolutely. It's debatable on desktop, but we have huge RAM now. Might as well error correct. The…
I won't bother on a desktop. I've been using 4 machines for the last 17 years with storage varying from 10GB to 2TB and RAM varying from 128MB to 16GB and haven't personally seen any kind of data corruption in motion (or at rest for that matter). Only had 2 mechanical drives fail (though predictably). ECC is costly. The memory modules itself and the board required to support it properly.
How would you know? Unless your computer use has been literally trouble-free (and all your archived data has been verified for correctness somehow), you can't know that none of your glitches over the past 17 years has been due to memory errors.