I'll go with one of the co-architects of ZFS, Matthew Ahrens,
There's nothing special about ZFS that requires/encourages the use of ECC RAM more so than any other filesystem. If you use UFS, EXT, NTFS, btrfs, etc without ECC RAM, you are just as much at risk as if you used ZFS without ECC RAM. Actually, ZFS can mitigate this risk to some degree if you enable the unsupported ZFS_DEBUG_MODIFY flag (zfs_flags=0x10). This will checksum the data while at rest in memory, and verify it before writing to disk, thus reducing the window of vulnerability from a memory error.
I would simply say: if you love your data, use ECC RAM. Additionally, use a filesystem that checksums your data, such as ZFS.
In other words, there is a non-zero chance that you will get silent data corruptions on disk if you don't use ECC RAM. It is the same risk with ZFS as with any other filesystem. And yet, personal computers have been running without ECC RAM for decades and it hasn't been a travesty. So yeah, if you are running in the type of situation where you absolutely must ensure the highest level of data integrity, then you must use ECC RAM. If you are running your own personal home media NAS, it is probably not an unmitigable risk to buy cheaper hardware. The storage gurus will argue, "Why use ZFS if you don't care about it's data integrity features?" My response is that ZFS has a ton of other very useful features that make it a great filesystem.
BTW, bad vs. good RAM is not the same thing as non-ECC vs. ECC RAM. While ECC RAM will protect you from bit flips, a bad stick of RAM is still a bad stick with or without the extra parity bit. Aaron Toponce has a good (non-sensational) discussion on the topic,