The speed skaters and curling teams of recent times have all harboured hopes of success but have ultimately come away with nothing.
Now the relatively unknown sport of bob skeleton has thrown up another contender and this time there may well be reason to cheer.
Alex Coomber heads into the Games fresh from having clinched her third consecutive world title this January.
"There is pressure on me but that's where I am - it's the situation I'm in"
The 28-year-old RAF intelligence officer is seen as Britain's best chance of making a mark on the medal table at Salt Lake City.
Coomber maintained her status as world number one by a single point following the World Cup meeting in St Moritz on January 17.
She could only muster fifth place in Switzerland, but that was enough to keep her top of the end of season rankings.
Coomber and GB team-mate Kristan Bromley will be feeling the burden of expectation as they head into Salt Lake.
Bromley, 29, will be competing in the men's skeleton and it is also hoped that he can finish in the medal positions.
But Coomber insists she will not allow the pressure to get to her.
"As long as a I train hard, prepare myself well and don't make any mistakes, then, whatever the result, I've got to be happy with that," she said.
"There is a certain amount of pressure on me but that's where I am. It's the situation I'm in.
"I just try not to get too bothered by it and just hope people realise all I can do is my best and anything can happen at the Olympics.
"Not many people know about skeleton in the UK and hopefully we're going to change that."
Coomber took up the sport four years ago after taking part in a novice weekend and found herself racing for Britain just weeks later.
The bob skeleton experience has been likened to sliding head first down a bobsleigh track on a tea-tray at 80mph.
In reality it is one of the toughest and most technical events in the winter sports calender.
Coomber explores every possible avenue to improve her times, from the technical design of her sled, to sprint training for her starts.
"Mentally and physically it's very demanding," said Coomber.
"It's a very intensive minute of concentration and when you add the physical side, getting up to 6Gs and 80mph its an awful lot for your body and brain to take on.
"This season I've been experimenting a bit more with runners, saddles, weights and starts to see if I can gain an extra two or three 100ths that can make all the difference."
One aspect of the Games Coomber has no control over is security.
September's terroist attacks on America had raised fears that Salt Lake City could be a target, but it is not something Coomber is dwelling on.
"I try not to think too much about it. I think that the security will be so tough and so strict that it will not be a problem," she said.
"Hopefully the Olympics will be a chance for America to show the world that they're not going to be beaten."
As far as the bob skeleton is concerned the same sentiments could apply to Coomber.