My predictions for the QF:
South Africa v Sri Lanka - Although SAF have never won a knockout yet, I feel they will better their record this time at the QF. I still feel they could potentially slip in the SF, but I feel they will do slightly better than their past history. And they have a good spinner Imran Tahir this time to counter SL. SL's bowling is pretty weak, and its time for SAF's pace to finally get one going against a good team.
Predicted Winner: South Africa
India v Bangladesh - Agree with what Poker said on this game. India have had two potential banana slip games (Ireland and Zimbabwe) and they should have come out pretty battle hardened out of those two games. And they are back in "now very familiar" Australian conditions. Their last game at MCG had such sensational fan support that a WC favorite like South Africa could not withstand the huge cauldron of opposition support and collapsed. Expecting the same fan support for this game (probably even more, since this is a WC knockout).
Predicted Winner: India
Pakistan v Australia - Rejuvenated Pakistan taking on massive WC favorites Australia, the team everyone dreads not to face early enough. Ideally Australia should sleepwalk their way through the next 3 games to lift the trophy on March 29th, but they will face the biggest two tests in the QF and SF, vs Pakistan and possibly India (if India make the semis). If Australia get past these two teams, this WC is theirs for the taking. But I have a feeling that Pakistan are getting close to prime form now and the inclusion of Sarfaraz has changed dynamics for them in a very positive way. This should be the biggest game of the quarterfinals, with it being very very hard to pick a winner. I am going with Pakistan here, also because this is at Adelaide which is the most subcontinental of all venues in Australia
Predicted Winner: Pakistan
New Zealand v West Indies - This is even more simpler to predict than the Ind v Ban game. WI have shown in their last few games that they have a long long way to go before they are considered serious contenders. Their inconsistency in the group stages was very frustrating. Even in the last game (vs UAE), they seemed to be in no hurry whatsoever (with rain looming). Their game looks very ordinary against good teams, and NZ should very easily get past them. Also the captaincy of Holder shows a lot of inexperience (the way he took the pedal off the accelerator against India proved it) and it could potentially bite them at a crucial stage.
Predicted Winner: New Zealand
If my predictions are right, a re-match of India vs Pakistan is coming up in the semifinals!
In that case, it would be the first time that Pakistan and India would be facing each other more than once in an ODI World Cup. They did so in the 2007 T20 World Cup. I would say India would probably want to face Australia than to face a 'back from the phoenix' Pakistan.