Google had done extensive studies[1]. There is roughly 3% chance of error in RAM per DIMM per year. That doesn't justify buying ECC if you have just one personal computer to worry about. However if you are in data center with 100K machines each with 8 DIMM, you are looking at about 6K machines experiencing RAM errors each day. Now if data is being replicated then these errors can propogate corrupted data in unpredictable unexplainable way even when there are no bugs in your code! For example, you might encounter your logs containing bad line items which gets aggregated in to report showing bizarre numbers because 0x1 turned in to 0x10000001. You can imagine that debugging this happening every day would be huge nightmare and developers would end up eventually inserting lot of asserts for data consistency all over the places. So ECC becomes important if you have distributed large scale system.
1: http://www.cs.toronto.edu/~bianca/papers/sigmetrics09.pdf