Top prospects by position
Catcher
Jesus Montero

We all know his potential. Has some of the best power potential in the entire minors and had 41 extra base hits last year in 105 games. Also led the farm system with hits (131) and had a .316 average, so he is not your normal slugger. The question with him remains whether or not he will remain behind home plate, and I personally don't think so. But as I've said before and will say again, it will have more to do with Austin Romine being so good than it will with Montero out growing the position.
ETA: 2012
Austin Romine

An extremely well rounded player who is good defensively but even better offensively. He has a very good swing and is given a ton of credit for his approach at the plate. Won't put up the biggest power numbers in the world, but they will be more than enough for a catcher. He hit .300 and dealt with a first half injury, then proceeded to hit 10 homers in the second half. Great potential.
ETA: 2012
Others to watch: Kyle Higashioka, Chase Weems, Francisco Cervelli
First base
Brandon Laird

Made the switch from 3B last year. Most of his potential has to do with his bat, which just oozes with power. He led the farm system with 23 home runs last year but was criticized for trying to hit homers too often, which led to his .273 average. He went on a tear for a good stretch late in the season, and his extra base hit numbers are excellent. Plenty of power potential. Now with Tex on the ML roster, Laird basically becomes nearly a non factor for the future other than maybe some DH at bats or a bench role to give ARod/Tex a breather.
ETA: 2012
Juan Miranda

Huge power bat, but he does most of his work against right handed hitters. Just like Laird, Miranda's future seems like nothing more than getting some ABs at DH against righties.
ETA: 2009
Others to watch: Nothing else to really pay attention to at 1B
Second base
Corban Joseph

A lot of ability with the bat because he has advanced plate discipline for his age, and it is good to see from a 2B. Solid defensively but nothing special. He did hit 15 doubles in short season ball, so hopefully some of that gap power can develop into home run power.
ETA: Late 2012
David Adams

Like Joseph, he was drafted this past June. He has higher upside but has a longer way to go to get there. His defense is shaky at times and his swing still needs work, but the right tools are in place for him to develop into a good player.
ETA: 2013
Others to watch: Jose Pierla, Damon Sublett
Shortstop
Carmen Angelini
Struggled a lot in his first full season for a number of issues including some injuries. But he is so young and has so much potential that it can't be ignored and he is still my favorite SS prospect in the system. What surprised people most were his struggles defensively, but even Jeter had 54 errors his first season out of high school. This guy has plenty of ability and I remain very confident in him.
ETA: Late 2011 at the earliest
Garrison Lassiter

A very good left handed bat at SS with potential for good power. Some question whether his defense will move him away from the SS position, but from whatever I have read it doesn't seem like his defense is so bad that it would force a position change. Very solid prospect, was a 2nd round talent who fell to us in June to the later rounds because of signability concerns, so there is clearly plenty of upside.
ETA: 2013
Others to watch: Jose Mojica, Ramiro Pena, Eduardo Nunez (I feel obligated to keep putting him here until he is 28 years old based on tools alone)
Third base
Brad Suttle

A very good all around player. He dealt with a number of injuries and even played through the same injury Posada suffered last season, so it shows his toughness. Although the injuries held him back some offensively, it didn't slow down his defense. He was excellent in the field and is a pure hitter. He is also a switch hitter which adds to his value and has a good power bat as well as the ability to hit for average.
ETA: Late 2011 at the earliest
Others to watch: Jimmy Paredes
Outfield
Austin Jackson

Depending on who you ask he is the #1 or #2 prospect in the system. Has turned into a great defensive player out in center but his arm is still average-above average. Has a beautiful swing that can lead to a lot of power potential (in the 20-30 range) and also has the speed to steal 30 bases a year. Can be an all around star who hits in the middle of the order.
ETA: 2009
Eduardo Sosa

Just 17 years old and sometimes people don't like putting such young guys on the same list as guys who have been playing well in the US, but what Sosa did in the DSL isn't what most other guys do. He displayed superior defense by all reports, and his offensive numbers don't lie. He hit .315 and had 27 extra base hits in just 63 games to go along with a ridiculous 30 stolen bases. Like any other young kid, he has to lower his K rate, but this kid is full of ridiculous amounts of potential.
ETA: Way too early to assume
Abraham Almonte

If it wasn't for such a terrible second half, this kid would be getting tons of recognition. Really an all around player who can hit for power and speed, but the switch from 2B to CF hurt him defensively and he has plenty of improvements to make in that regard
ETA: 2012/2013
Kelvin De Leon

Was the top offensive international FA last year when we signed him along with Eduardo Sosa. The reason he's fallen behind Sosa doesn't have to do with De Leon's poor performance, but the fact that Sosa played so well. De Leon is solid defensively in the corner OF and showed more power than Sosa. However, he is not a speed demon like Sosa (although by no means is he slow) and his average wasn't over .300 (.289). However, I think the potential for both is similar, but Sosa is better defensively at a more important position and shows top flight speed.
ETA: Same as Sosa
Others to watch: Colin Curtis, Carlos Urena
Starting Pitchers - This is the Yankees and this is an area we are absolutely loaded, #1 in ERA and WHIP as a minor league system last year and I really don't see why it won't happen again. At all levels there are top prospects...
Dellin Betances

Struggled in the first half then dealt with an injury, but for the first time in his professional career he put it together over a long period of time when he returned. In 115.1 innings at Charleston, he struck out 135 and only allowed 87 hits. His achilles heel as usual is 59 walks. But down the stretch in his last 8 starts in 55.1 innings, he had a 2.91 ERA and 0.94 WHIP. He is still incredibly young at just 20 years old and the sky remains the limit, and he enters the second consecutive season as our top pitching prospect IMO due to his mid 90s fastball and a much improved and useful changeup as well as a sharp 12-6 curveball coming off of his 6'9'' frame.
ETA: Late 2011/2012
Andrew Brackman

Similar to Betances because of their height and fire fastballs. He finally debuted in the Hawaiin Winter League after missing last season while recovering from TJ surgery. What give people a lot of hope about him is not just his size or fastball, but his plus curveball which leads to many Ks. The sky is the limit for him.
ETA: Sometime 2010, we'll know better as he gets innings in the minors
Zach McAllister

My favorite pitching prospect because I have been on him for 2 years when people weren't giving him much credit, so naturally I find myself defending him now

ETA: 2011
Jairo Heredia

Another one of my personal favorites, so I may have him ranked higher than others. As a very young 18 year old in A ball, Heredia had a 3.25 ERA and struck out nearly a batter per inning. Has a sick curve and a changeup that is catching up fast, and has excellent command of all his pitches. Many believe he can still add to his fastball because he is so young and so skinny, and if he does then he will really grab attention from scouts.
ETA: Late 2012/2013
Christian Garcia

Same story as last year and every other year. He has had multiple surgeries including his knee and Tommy Johnn, and countless other DL stints. If he remains healthy he can be a star because of his ridiculous stuff, which scouts was agreed was better stuff than Phil Hughes' when he was the #1 prospect in all of baseball. He battled injuries again last year but put up a very good K rate, but is still a work in progress and is already 23 years old so time may be running out on his potential.
ETA: 2010
Manny Banuelos

Just 17 years old and left handed, Banuelos pitched very well in the GCL last season. Some are higher on him than I am, but I am certainly not low on him since I am considering him one of our better prospects at just 17. He has plenty of potential, I am just not ready to say he better than some other guys. Scouts like his maturity and poise as much as his stuff and command, so maybe that is why I am not as high on him because I am unable to see those things. But any teenage left hander who is mature and puts up stats is one to watch very closely.
ETA: Too early to say
Arodys Vizcaino

I may be in the minority, but I like him more than Banuelos. He reminds me a lot of Heredia in terms of his stuff and his attitude, but he lacks the command to be considered a top prospect just yet. He throws very hard (tops out at 92-94 mph already) and just turned 18 a month ago. In the GCL he struck out over a batter an inning and less than a hit per inning.
ETA: Too early to say
DJ Mitchell

Drafted out of Clemson this past June, Mitchell signed too late to get any action with the minor league clubs. He is a very good athlete who throws two good fastballs, a quality curve, and a changeup that he has already improved a lot. Should be fun seeing him in action this season.
ETA: 2011/2012
Wilkins De La Rosa

He isn't a top prospect but I wanted to put him here instead of "others to watch" because he is worthy of a long discussion. Switched from OF to pitching, the left hander really dominated this season. He pitched 106.2 innings between Low and High A, and finished with a 2.11 ERA, 1.09 WHIP, 125 Ks, only 72 hits allowed, and an amazing only 2 home runs allowed. Not bad for a left hander who just learned how to pitch. He will be 24 when next season starts so he can move quick, and he is hard to get a grasp on because of the lack of pitching track record so people don't know what to really expect, but the potential is obviously there. He throws a change and slider as well, with his change being his best secondary pitch.
ETA: Late 2010/2011
Others to watch: Jeremy Bleich, George Kontos, Mike Dunn, Brett Marshall, Ivan Nova, Nik Turley
Relief Pitcher - I put pitcher instead of pitchers, because there really is just 1 guy to focus on
Mark Melancon

He dominated all three levels of the minors in his first professional season and off of his return from TJ surgery. In 95 innings he had a 2.27 ERA, 0.95 WHIP, and allowed 69 hits, 22 walks, and 89 Ks. Some were worried about his innings amount coming off the surgery as a reliever, but guys he played with called him the most efficient pitcher they have ever seen. He literally had innings where he would throw 6 or 7 pitches, so they had to keep putting him back out there in order to get his pitch count up. Sometimes he went 3 or 4 innings but only threw 25 or 30 pitches. And he didn't strike out less than 1 per inning because he doesn't have the stuff, he can strike more guys out if he wanted to but he realizes as a reliever he needs to be efficient because he might have to pitch any given day. When needed, he can strike anybody out. Instead, he goes out there and lets hitters pound his sinker into the ground on the first pitch. He has a mid 90s 4-seamer, a low 90s sinking fastball, a very very hard/sharp curveball, and his change came out of nowhere. He isn't like most relievers who have 2 pitches. He also isn't like most relievers in his maturity. He has some of the best make-up that scouts have ever seen, absolutely destined for the closer's role. A real stud of a prospect.
ETA: 2009, maybe even right out of spring training
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My personal top 25 list:
1. Jesus Montero
2. Austin Jackson
3. Dellin Betances
4. Andrew Brackman
5. Mark Melancon
6. Austin Romine
7. Zach McAllister
8. Jairo Heredia
9. Christian Garcia (last chance for him as a top 10 prospect)
10. Brad Suttle
11. Brandon Laird
12. Arodys Vizcaino
13. Manny Banuelos
14. DJ Mitchell
15. Wilkins De La Rosa
16. Jeremy Bleich
17. Eduardo Sosa
18. Abraham Almonte
19. Carmen Angelini
20. George Kontos
21. Kelvin De Leon
22. Corban Joseph
23. Brett Marshall
24. Juan Miranda
25. Damon Sublett
It is no accident that 13 of the 25 are pitchers, and it isn't due to a lack of good position players but an excess of awesome pitching prospects
Guys I kept off the list because I don't consider them prospects at this point: Ian Kennedy (more of a prospect than a ML player, but not worth wasting a spot on him because we all know about him), David Robertson, Brett Gardner, Alfredo Aceves, Phil Coke, Humberto Sanchez, Francisco Cervelli. All of these guys could have fit in the top 25 somewhere.
Add your own lists or discuss anything you'd like, this is the fun and less stressful area of the organization, so lets enjoy it