This question is regarding check-in, not carry-on, baggage.
I'm considering buying a very spacious suitcase measuring 31 x 21 x 15 inches, for a total of 67 inches. This is greater than the 62-inch limit most airlines have . My present suitcase measures 63 inches, which better fits the limit than the one I'm considering buying.
Do airlines actually enforce the size limit for check-in baggage, such as by levying a surcharge? Has this happened to you or to someone you directly know, or is it only a theoretical risk? If it's only a theoretical risk, I'll buy this suitcase.
I've had my check-in suitcase weighed several times, but never had its dimensions measured, as far as I can remember.
 Except for Emirates, which recently decreased its limit to 59 inches.