I have a client who insists on using the following sentence in his web site:
Lance Armstrong is the most successful American bike racer of all times.
I think that "of all times" should be "of all time".
Which is correct?
"Of all times" and "of all time" are different expressions. They are both in vogue, both are correct, but they mean different things.
The phrase most appropriate for your situation would be "of all time." "Of all time" is used to make a comparison, stating that something is the best throughout the ages.
"Of all times" has a different meaning and usage. "Of all times" is used to mean the wrong time. For example:
Thus, if your friend were to write "of all times," he would be using a wrong expression--still an expression, but the incorrect one in this case.