Bayern Munich v. AC Milan
I believe this will be close, but AC Milan will pull it out.

Benfica v. Liverpool
Liverpool, obviously

Real Madrid v. Arsenal
This one is tough. Real have been struggling this last month and it will all depend on how they come back after christmas. I think Arsenal will advance, but it is really a toss up.

PSV v. Lyon
It seems you guys are favoring Lyon, but i PSV will give them a run. Lyon will win but it will be tougher than believed.

Chelsea v. Barcelona
Again, this is a toss-up, but between two much better teams. Both teams are leading their leagues and are playing well. I think Barcelona will prevail, since Chelsea hasn't been as dominant these last couple of months, as seen by the losses to Real Betis and Man U and a tie against Everton.

Rangers v. Villareal
I don't know a lot about either team. I know rangers seem to be struggling this year in the scottish premier league, while villareal are lurking behind barca at 4th place. I think Villareal will win this matchup.

Bremen v. Juventus
I think Juventus easily wins this match.

Ajax v. Internazionale
This is another matchup i am a little fuzzy about. Inter seem to be doing well, sitting second in Serie A while Ajax sit in fourth in the Holland League. I think Inter wins in a close matchup.

That leaves:(These are predictions, if the matchups ended this way. I don't know how they will fall, but these are my predicitons based on the above predictions.)

Arsenal v. Inter
Inter wins close.

Barcelona v. AC Milan
Barcelona prevails.

Juventus v. Liverpool
I believe Juventus will win this matchup. Liverpool will put up a fight but Juve is very strong throughout.

Lyon v. Villareal
Villareal will play closely to Lyon, but Lyon will eventually prevail.

Now:
Inter v. Barcelona
Barcelona wins.

Lyon v. Juventus
I'm not sold enough on Lyon getting past this point. Lyon will play close for a while, but Juve would eventually pull away. This may change, after i get a chance to see Lyon play again, but right now it would be Juve.

Championship:

Barca v Juve
This would be the best game of the whole tournament. These teams are very similar, but again Juventus seem unstoppable to me. They are playing very well together and have a good chance to win.

Although this is a little long, it's just my insight. I look forward to watching the future games.