Fairly stable is not the same as completely stable. Lots of things can mess up in RAM - heat, failing chips, cosmic radiation, gremlins, unstable power. It may only mess up one in a few trillion trillion times - but RAM is reading and writing millions of bits a second.
ECC RAM is designed to be able to catch those failures and fix them. For a server, this is important, because it can mean the difference between continuing to run or crashing. Or the difference between your paycheck being $1000 or $100. It also allows the server to watch for RAM that is starting to fail.
The performance difference is fairly small - 2-3% or so I believe. Not enough to be noticable. Your server crashing because of bad RAM is however very noticable.
If it is not a critical system - doesn't process financial records, some downtime or even data corruption is acceptable, etc, and you are on a budget, Non ECC RAM is fine. But for most applications, the extra expense is worth it for the added reliability.