Manchester United vs Real Madrid
So many subplots in this matchup. Ronaldo returns to United, Fergie's possible heir vists Old Trafford. This was probably the matchup everyone was hoping for simply because of the subplots and after that, the teams themselves. United's defense is still suspect and we all know what happens when Ronaldo is given even a sliver of time and space. This one is probably fairly even and could go either way in the end.
Barcelona vs AC Milan
A rematch of both the Group stage and Elite 8 from last year. The main difference being that there's no Ibrahimovic on Milan. While Milan is a shadow of what they were last year they might have the most intriguing player in El Sharrawry, who has been resposible for most of Milan's success this season. I don't think this will be anywhere near the level of play from last year and Barca should easily get through Milan.
Juventus vs Celtic
How easy should it be to write off Celtic with this matchup? It shouldn't considering The Hoops were given less than no chance of even finishing 3rd in the group stage. While Juventus is clearly the better team, you need to remember that Celtic almost took 4 points off of Barca if not for a late late goal in the Nou Camp and if the Celtic-Barca matchup had been in the Knockout stage, they would have gone to extra time and possibly penalties. It'll be a mountain to climb for Celtic if they hope to advance, but it's not impossible and Juve should be cautious otherwise they could be the next giant that The Bhoys slay.
Bayern Munich vs Arsenal
I don't see this matchup in the same way as Si. This could be the most competitive tie of the Last 16. And considering Arsenal actually was the third team picked out of the pot, with Barca, PSG and Dortmund still up on the board, it could have been worse for them. While Bayern is clearly the best team out of the Bundesliga right now, and much improved over last year's squad, this is by no means an easy pass for the Bavarians. You have to remember that despite the Gunners roller coaster league form, they've excelled in the Champions League(albeit against significantly lesser opponents than Bayern). Arsenal can push forward if they make the right moves both on and off the field. This matchup has the best potential to go all the way down to the wire.
Borussia Dortmund vs Shakhtar Donetsk
This one is equally tough, especially considering Shakhtar came a goal short of actually winning their group which included Juve and Chelsea. Both teams are dark horses, Dortmund less so, and both involve brilliant managers, according to ESPN it's basically the Old Sage(Lucescu) vs the Mad Scientist(Klopp). This matchup may prove to be entertaining and could, just like Man U-Madrid and Bayern-Arsenal, go either way.
Malaga vs Porto
This matchup features possibly two players who are future superstars, Isco and James Rodriguez, and both boast bright futures provided they don't lose key players. Malaga was a victim of the same careless spending that City and PSG are somehow pulling off and it cost them some good players, i.e. Santi Cazorla, and Porto is the Portuguese "Arsenal" in some opinion circles. Porto, just like Shakhtar came oh so close to winning their group and as a result may have been given a seriously tough challenge to make it through to the next round.
Schalke vs Galatasaray
I think we all can agree that this matchup is gonna be fueled by the passionate fans of both clubs. Galatasaray managed to stumble their way into the Last 16 and could be in for a tough 2 games against a dangerous Schalke side, who've been struggling in the Bundesliga. Both teams have talented and dangerous strikers, Galatasaray has Burak Yilmaz and Schalke has Klaas Jan-Huntelaar(remains to be seen if he'll still be a member of Schalke beyond January). If the matches are boring I'm sure we'll have plenty of entertainment from the fans.
PSG vs Valencia
It's essentially Valencia vs Ibrahimovic. PSG has spent ass loads of money to build a team that can compete with the best in Europe, I actually believe they've done a good job too, but they still heavily rely on their Swedish Striker to bail them out of bad predicaments. As for Valencia, they're in the same boat as Schalke and to a lesser extent Arsenal, good performances in the Champions League and struggles demestically failing to string together consecutive victories so far. Valencia's defense needs to step up as well, they've conceded 30 goals in just 25 games overall this year and when you go up against a team where their best player(who is arguably the 3rd, maybe 4th, best player in the world) can score from practically anywhere and anyway, you need to defend really well to have a chance.
My picks: Real Madrid 4-2, Barcelona 6-1, Juventus 3-3(away goals), Bayern Munich 4-3(extra time needed), Dortmund 5-2, Malaga 2-1, Schalke 3-1, PSG 7-2