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The Irish, who produced one of the upsets of pool play with a 15-6 victory over two-time champions Australia, have never advanced beyond the quarter-final stage, which they have reached on no fewer than four occasions.
Wales claimed third place in the inaugural World Cup in 1987 after being smashed 49-6 by New Zealand in the semi-final, but have achieved nothing better than Ireland since then.
Given the two teams' such woeful records in recent World Cups, it is not surprising that Ireland captain Brian O'Driscoll refuses to look too far ahead.
"Why would you even contemplate thinking about a semi-final or the prospect of a final when you've got a quarter-final this weekend?" O'Driscoll asked.
"If we don't win this weekend we're on the plane home. We've got way too much respect for Wales to be looking beyond them."
Ireland coach Declan Kidney has been left sweating on the fitness of hooker Rory Best, who suffered a shoulder injury in last week's 36-6 victory against Italy and was bracketed alongside Sean Cronin in the Irish team announcement.
Kidney has stuck with his half-back pairing of Conor Murray and Ronan O'Gara after the duo starred when united for the win over Italy, although he has proven bench cover for the pair in scrum-half Eoin Reddan and fly-half Jonathan Sexton.
Ireland have won nine out of their last 12 Tests against Wales but were beaten 19-13 when the teams last met in Cardiff in the Six Nations in March.
And Wales skills coach Neil Jenkins admitted that Ireland were a side capable of posing problems.
"They are pretty strong all round," Jenkins said.
"They are a very tough physical side with a huge amount of talent in the backline and a tough, physical forward pack as well.
"So we just expect an all-round very tough game, very good in the set piece. They can score tries, as well. So it's going to be a very tough game for us.
"(But we're in a very good position. We've got a lot of strength in depth, but it's a nice selection headache to have."
Ireland wing Tommy Bowe, who plays his club rugby in Wales for the Swansea-based Ospreys, said he expected a "ding dong battle" against their northern hemisphere rivals, who hit a rich rein of form to emerge second from a tough pool involving champions South Africa, Fiji and Samoa.
"We'll be expecting them to be playing an expansive and exciting game of rugby," Bowe said.
"We know how well Wales are playing at the minute. They're definitely one of the form teams in the World Cup. It's going to be a tough match.
"Hopefully the rain stays off because we'd be wanting to play a bit of rugby also. I think it's really up there for a ding dong battle."
