I agree with the other comment about there being a lot of predecessors to IEEE floating point numbers. What happened was that when people designed other, non-IEEE floating point arithmetic, they sometimes got things wrong. Not wrong in that the hardware produced incorrect results, but that it was hard for people to write code that did what they wanted. The dominance of IEEE floating-point numbers (in part due to the fairly logical way it's designed, and at the time they took into account what they knew, about 40 years ago now) means that we have all forgotten how annoying things can be if you don't have IEEE numbers.
One of the well-known people in this research area is Bill Kahan, and on his webpage (http://people.eecs.berkeley.edu/~wkahan/) he has a bunch of, uhm, rants about floating-point arithmetic. If you read some of them, you can find clear explicit examples of arithmetic that's not IEEE-compliant, and does weird hard-to-understand confusing things that don't really happen any more. (For example, p.4 of http://people.eecs.berkeley.edu/~wkahan/Mind1ess.pdf, and you can dig around his page for more examples; none of these were done out of malice by programmers, they just didn't think things through, which is what Kahan is writing about)
One of the well-known people in this research area is Bill Kahan, and on his webpage (http://people.eecs.berkeley.edu/~wkahan/) he has a bunch of, uhm, rants about floating-point arithmetic. If you read some of them, you can find clear explicit examples of arithmetic that's not IEEE-compliant, and does weird hard-to-understand confusing things that don't really happen any more. (For example, p.4 of http://people.eecs.berkeley.edu/~wkahan/Mind1ess.pdf, and you can dig around his page for more examples; none of these were done out of malice by programmers, they just didn't think things through, which is what Kahan is writing about)