There is a significant amount of anecdotal evidence that supports the claim that, not only did this happen once, but that it happens rather frequently. Unfortunately, most of these claims appear to come from members of the security industry, which may have a vested interest in convincing people that this type of activity is taking place.
The type of theft you're talking about is called salami slicing. There have been a number of papers published on this attack by security researchers (not peer reviewed, mind you), such as this one and this one. This second paper repeats a variation of what is probably the most famous claim: a former bank employee in Canada who stole $70,000 using this type of attack. Unfortunately, the papers are lacking in details, and the references don't match the contents.
The most often quoted (and not cited) source for these claims seems to be this Network World article, which recites a list of supposed convictions based on salami-slicing techniques. Again, it's lacking in details, though it does give dates and jurisdictions for several purported cases of salami slicing.
Overall, my intuition tells me that micro-theft of this sort has certainly occurred at some point in the past. It's really nothing more than a modernized version of clipping coins, which certainly happened on a regular basis. However, I cannot find any evidence of any single, famous, and verifiable case of salami slicing that matches the circumstances usually supplied in the anecdotes you mentioned.
On a related note, there's much better evidence regarding similar kinds of salami attacks, just not ones involving bank employees. For example, this Wired article describes a man who allegedly defrauded E*Trade using a variation of a salami attack (related to how the brokerage firm verified that it could deposit money into your account), including links to a Dept. of Justice affidavit describing the attack. There was also a case in Florida of a rental car firm overcharging customer for tiny amounts of gasoline on returns.