[gilgoomesh]

The computer programmer in me says both are valid:

"on accident" is a pre-prepared behavior that will be employed when an accident occurs in the future.

"by accident" is metadata accompanying an event, reporting the author or agent that created the event.

[efaref]

It sounds like old-style BASIC exception handling.

    ON ACCIDENT GOTO EMERGENCYROOM

[TeMPOraL]

Or modern JavaScript event handling. Button.onAccident(function() { ... });

[unfamiliar]

Except that's not how it is used, it is used in place of "by accident."

"I knocked over the glass on accident."

[twcooper]

In the first case, it would be more clear to say "upon accident."