While there are many great competitors in recent memory that come to mind, my personal choice for greatest ever women singles competitor is Katarina Witt. I cant think of anybody else who came up with any many clean performances under the most intense pressure. There is a reason that women has won 6 of the 7 World/Olympic titles from 84-88. When she skated before a chief rival, or more then one chief rival she would put down something that dared you to beat her. Usualy her chief competitor to follow would blink, happened to Sumners in 84 Olympics, happened to Chin at 85 Worlds, happened to Ivanova at the 85 and 86 Europeans to think of a few examples. When she skated right after a chief rivals strong performance she would rise to the occasion and trump them as she did to Ivanova at the 85 Worlds, as she did to Kadavy and Thomas at the 87 Worlds. She also was able to intimidate her competitors in warmups and practices, she was a master at taking charge when in the vacinity of her competitors, and manipulating the setting to her advantage, also getting inside their heads.
For the men I would have to say Elvis Stojko would be my first choice. Again very rare for him to crack under pressure one bit. Only at the 93 and 96 Worlds in the short program did this happen during his prime of 91-98(well 91-93 were probably not really his prime but when he was healthy). The tougher the situation, the higher the pressure the better he performed. At the 95 Worlds I recall him skating with a major injury occured at practice for the 95 Canadian Nationals. He skated an excellent short program while struggling to land the triple axel all week in practice, one of only 2 guys to do the triple axel-triple toe and ended the short in contention for the gold in 2nd place behind Todd Eldredge(the only other guy to do a triple axel-triple toe). In the free skate Todd had already skated and made a couple of mistakes, downgrading a triple axel-triple toe to a triple axel-double toe and falling on a 2nd triple axel attempt, however Todd finished with a flurry by throwing in an unplanned 3rd triple axel attempt and completing that 2nd triple axel he missed in his first go around. Elvis was under considerable pressure but turned in a brilliant performance on that gimpy leg, with the clincher late upgrading a final triple lutz combination to a triple lutz-triple toe, giving him 8 clean triples to Todd's 7 and 2 triple-triples to Todd's 1 and his 2nd straight World title on a 6-3 split. Some who saw him practice doubted he would even finish the event. Then the 98 Olympics, who can remember that, barely able to walk when the event was over, but determined to skate in the Olympics landing 8 triples and the silver medal, unbelievable. Of course it might have been as foolish as foolhardy as he was never the same skater again as he ended a fairly(for his standards)ordinary final 4 years to close out his career dealing with the aftermath of the injury and younger superstars like Yagudin and Plushenko. I also must point out the 97 Worlds where skating a clean short program where the top 6 contenders all skated cleanly, the quality of the competition left his own excellent skate in 4th place behind Urmanov, Eldredge, and Kulik. Putting aside any self doubts, frusteration, and any dissapointment from that he blew the field away technicaly with the quad toe-triple toe(which he himself landed the first ever of at the GP final a couple months prior)and 8 total clean triples to go with it, and jumped from 4th to 1st; after Eldredge needing to land all 8 triples in his quadless program to have any chance missed his final triple axel attemp twice under serious pressure from the Stojko barrage earlier.