It seems that the era of "Joe's guys" may be coming to an end and we'll see players on the field based on their talent.  According to the Times today, some younger players with better spring performances are expected to make the roster over older, "trusted" players.
Nieves/Pratt/chair cushion is a tossup for backup catcher, since all of them hit under .200 this spring, and will have to be addressed with a trade during the season.  However, at first base it looks like Josh Phelps will get on the roster over Andy Phillips:

Phelps is a year younger than Phillips, who turns 30 next week, and he has 210 more games of major league experience, with a better career average (.268 to .228) and more power. Playing last season at Class AAA Toledo in the Detroit farm system, Phelps batted .308 with 24 homers and 90 runs batted in....
Phelps is batting .400 with 3 homers and 10 R.B.I. He has three seasons in the majors with at least 15 homers.

In the bullpen, Sean Henn will likely be a middle lefty over Ron Villone:

Villone signed a non-guaranteed contract that calls for him to earn $2.5 million if he makes the opening-day roster. Because he costs so much more than the rookie Henn, Villone had to pitch better than Henn to make the roster.
Instead, he has pitched worse, with a 14.40 earned run average. In nine games, opponents have batted .520. Henn has a 3.00 E.R.A. and a .182 opponents' average.

I'm not sure about Henn, but this was still a no brainer- the last couple days, Villone had the dreaded "0.0 IP, pitched to x batters in the nth" in the box score.  It's nice to see that there is some point where you can be so bad that you can lose your place as one of Joe's Guys.  It's a little sad because one reason Villone may be so terrible now is due to Joe burning him out last year.
Most importantly, it looks like CashMan is stepping in and making Joe a little more sane on these sorts of decisions:

The additions of Henn, Nieves and Phelps represent a subtle organizational shift. Villone, Pratt and Phillips all fit the classic Torre profile because of their experience. But General Manager Brian Cashman wants to make the team younger and cheaper, and Torre is on board with that.

We'll see whether this translates to things like bullpen usage during the season and whether Joe can finally start using more than 3 relievers in a given week.

Update, 12:15pm: Selections confirmed at yankees.com. Karstens will start on the DL, Bruney and Rasner also made the team. Your 2007 New York Yankees:

SP: Pavano Pettitte Mussina Igawa Rasner (Replaced by Wang in 4 weeks)

RP: Myers Henn Bruney Vizcaino Proctor Farnsworth Rivera

OF: Matsui Abreu Damon Cabrera

IF: 1B: Mientkiewicz, Phelps, Giambi (DH) 2B: Cano SS: Jeter 3B: Rodriguez IF: Cairo C: Posada, Nieves