Giguere's unbelievable play got Anaheim all the way to Game 7 of the Stanley Cup final that spring and earned him the playoff MVP award, but the furry growth of hair all over his face is just as memorable for some.
"I remember it was big," said Samuel Pahlsson, one of Giguere's teammates then and now. "That beard was huge."
This year's playoff performance by Giguere has so far looked pretty similar to 2003 - until he takes off his mask, anyway.
The 30-year-old is clean shaven this time around and might very well be as for ID if he were to try to purchase a bottle of champagne. Giguere's playoffs ended with a loss four years ago so he's not concerned about bucking one of hockey's noted traditions this post-season.
"If you do a superstition you might as well win with it and we didn't win," he said after practice on Friday. "You've got to change something sometimes."
It's hard to argue with the results so far.
With a 2-0 series lead over Ottawa heading into Game 3 on Saturday night, the Ducks are clearly the most relaxed team in this Stanley Cup.
That doesn't mean that Giguere or any of his teammates are taking anything for granted. They're simply enjoying the experience.
"We have a lot of fun as a group," said forward Todd Marchant, whose thick red beard conjures images of Lanny McDonald in his later years. "We laugh at each other, we make fun of each other - it's all in good fun."
Part of that fun involves talk of facial hair.
While guys like Giguere and defenceman Chris Pronger purposely sport the clean-shaven look, others like Pahlsson and 22-year-old Corey Perry have little choice in the matter.
Marchant remembers being a young player with the Edmonton Oilers and yearning for the sort of playoff beard he has now.
"Ten years ago when I was in my first Stanley Cup playoffs, I don't think I could grow anything," he said. "I looked like Corey Perry."
Veteran forward Brad May is one of the Ducks greybeards - both figuratively and literally.
His 15-year NHL career had never taken him past the second round of the playoffs before this spring so he's entered some new territory with his facial fuzz.
"I've never played long enough to get any steam with it," said May. "I've actually trimmed it down a few times this year."
The tradition of growing playoff beards is often credited to the New York Islanders teams that won four straight Stanley Cups in the early 1980's.
Almost all of the Ottawa Senators are currently sporting some facial hair and many of the Ducks are as well. None of them is doing it to make a fashion statement.
"It's just about tradition," said Marchant. "It's nothing more than keeping the tradition alive."
It might seem like a silly way of commemorating how far your team has advanced in the playoffs, but those close to the game know that it might be the only chance most of these players get to do it.
"We're in a unique situation competing for the Stanley Cup," said Ducks coach Randy Carlyle. "There's some people in the room, coaching staff involved, that have been involved in the pro games for 30 years, and this is our opportunity."
Like Giguere and Pahlsson, Ducks forward Rob Niedermayer is getting his second chance.
He has again grown a thick beard during this playoff run and is in no hurry to get rid of it.
"I think after maybe five, six days you get past that itchy point," said Niedermayer. "It's fine. You don't even notice it too much."
That doesn't mean he'll be keeping it after the Stanley Cup has been handed out - no matter who wins.
Niedermayer is scheduled to be married this summer and his fiancee isn't a fan of the look.
"I'll probably have to shave it right away I'm sure," he said. "She's having none of it."
Teammate Travis Moen will probably be standing at the sink first.
He describes his current look as "a little weak on the sideburns but strong in the front" and won't be sad to see it go.
Of course he didn't really even have to go there in the first place.
The Ducks have no problem with some in their ranks going clean shaven - even the once-grizzly bear Giguere.
"You don't win because you have a beard, you don't win because you put your left skate on first, you don't win because of superstitions," said May. "You win because you work hard and you do the right things."