Writer's Note: MikeFive and I discussed something about this a few weeks ago, and I said I was going to look into it and write about it in a few days. Then I never finished it, but Geoff's post about 2004 reminded me of it. I had left off at the 2007 draft, and frankly it's too soon to say anything about 2008, 2009, so I'm just publishing it as I left it.
This is totally and completely appropos of nothing whatsoever. It merely came up in conversation a few weeks ago and I started to look it up and realized I should just do it the right way.
Note, their are footnotes in this article. (And in my best David Foster Wallace-ness, one footnote to a footnote.) Information, unless otherwise cited, came from [http://www.prosportstransactions.com/hockey/DraftTrades/####.htm] (replace "####" with the year (eg: "2001") you want to look at).
1st Justin Williams (28th)
2nd Traded to Carolina as part of Keith Primeau acquisition
3rd Alexander Drozdetsky (94th)
Williams is a veteran NHL player who's been named to the All Star team; that's a successful late first round pick. Drozdetsky was pretty much unseen heading into the draft but was believed to have fallen further than he should've due to the mystery. This was basically a risk pick that they hoped would be would out. He never left Russia.
1st Jeff Wywitka (27th)
3rd Patrick Sharp (95th)
The Flyers swapped down four spots with Ottawa in exchange for a 2nd round pick in the 2002 draft. Ottawa used that pick to take Tim Gleason. The guys selected between them never made the NHL for more than a year. Not a great pick, but they didn't really miss out on anyone, either. The Flyers traded him two years later in the ill-conceived Mike Comrie trade (more later).
The second round selection was traded straight up for 32 year old Jiri Dopita. He went on to play 72 NHL games for the Flyers and Oilers in two seasons before going back to Europe. The Flyers traded him after the season to Edmonton for a 3rd round selection. So they gave up the #56 in 2001 in exchange for a season of Dopita and the #87 in 2003 (Alexandre Picard). Fair enough.
In the third round, the Flyers had made a deadline deal in March sending the 2001 #88 for 28 year old Dean McAmmond. In June, they flipped McAmmond for the #105 in 2002. Good deal. Patrick Sharp was their own pick and obviously a good choice.
1st Joni Pitkanen (4th)
2nd No selection, incredibly. 
The Flyers traded up to get Pitkanen, giving Tampa Ruslan Fedotenko, the 2002 #34 and #52. Not a great deal, but Pitkanen certainly has lived up to being a #4 pick.
As for the third round picks, pure genius. One of them (#70) was acquired for Andy Delmore the previous summer, then flipped on draft day, with Brian Boucher, for Michal Handzus and Robert Esche. The other one (#92) is the last piece of the Oates trade.
Quite the draft. The Carter pick was acquired from Phoenix for Daymond Langkow. No story behind the Richards selection. It was the Flyers own pick that year. Though this was a great draft, keep in mind this was probably the greatest draft class in NHL history. 
In the third round, Colin Fraser took a while to develop, but has played 135 games for the Chicago Blackhawks last season and this season and is a solid NHL contributor.
The Flyers also did pretty well with their three out of seven picks in the third round. Picard is closing in on 200 NHL games played and is a third pairing defenseman. Potulny is closing in on 100 NHL games played and is an extra man on an NHL roster. Ruzicka was a good AHL player who never got it together to make an NHL roster and went back to Europe.
Rick Kozak has average 3.4 PIMs in his last four seasons in the CHL. His career highlight reel is hosted at hockeyfights.com, which I think is all we need to know about him.
3rd Rob Bellamy (92nd)
Ugh. The first pick was part of a package for Mike Comrie that turned disastrous in record time (he was gone in less than two months). 
In the second round, the Flyers' had obtained the Kings pick (#41) for Roman Cechmanek, but traded it in the package for Alexi Zhamnov from Chicago. Their own pick was traded to the Coyotes in a package for Tony Amonte, then sent to the Rangers who chose Brandon Dubinsky with it. Double Ugh.
Bellamy has been playing with the Phantoms the last two years, without impressing.
This was the post-lockout snake draft.
1st Steve Downie (29th)
The Flyers traded down nine spots with Florida and obtained a the #41 pick in the following year's draft. The players I recognize who were selected between those picks were: Tuuka Rask, Niklas Bergfors, TJ Oshie, and Andrew Cogliano. Downie is as good as any of those forwards and is a solid NHL player, so this was a pretty good deal.
The Flyers' second round pick went to the Rangers (with the aforementioned brawler Rick Kozak) for Vladamir Malakhov. The Flyers traded Todd Fedoruk for the #59 before the draft, then traded out of the round swapping that pick with Phoenix for the #119 and what turned out to be the #39 in 2006. Thats a good deal.
The #81 was part of the Comrie package (and became Danny Syvret). They also had Dallas' pick for Chris Therien, which they traded out of sending the #89 to #102 to Tampa for their second round pick the following season, which was the #47. Another pretty good deal.
Claude Giroux is a good pick.
In the second round, the Flyers had that #39 from Phoenix and took Nodl. His verdict isn't quite in, but it looks like he's going to be an AHL player. If that's the case, it's not a good selection. The Flyers got the #42 from the Kings when Dean Lombardi became their GM, and took Ratchuk. He's also not looking good to be in the NHL. Bodrov is the Flyers' own pick, who just the other day finally came over from Russia and isn't looking too promising. Those fist two selections could've instead taken Milan Lucic (#50). Having all three second round choices bust is not good.
In the third, the Flyers had the #66 from Chicago for Patrick Sharp, then traded down with Montreal turning it into the #79 and the #109 (fourth round). They took Matsumoto with that Montreal pick. Then sent their own selection to the Sharks for Niko Dimitrakos. Dimitrakos played 25 NHL games and is now in the Swedish Elite League. The Flyers also had Nashville's #86 in exchange for Danny Markov, then used it to get former employee Dean Lombardi and the Kings to eat Jeremy Roenick's salary. Matsumoto is still a question mark, the Flyers got under the cap after signing Forsberg, not a bad round....
1st JVR (#2)
2nd Kevin Marshall (#41)
JVR seems to be living up to being the #2 overall.
Their second round pick, #31, was traded straight up for Marty Biron. They traded up to get Kevin Marshall at #41 by sending Washington the #84 and the 2008 #58.
 The Flyers at one point owned four 2nd round selections in this draft, and two third round picks. Forget (until we get to Jeff Carter) about how they got those picks (its absolutely insane) and let's just deal with what they did once they had them. A pair of the 2nds went to Washington in the allegedly stupid Adam Oates trade.[a] The other two 2nds went to Tampa in the trade for the #4.
[a] Have we ever actually revisted the Adam Oates trade? The Flyers gave up:
1) Maximme Ouellet, who appeared in 12 NHL games for three teams and is out of hockey.
2) Their 2002 1st (#26), which Washington then combined with the #42 and the 2003 #185 to move up 13 spots to #13. Dallas used it to select Martin Vagner who never left Europe. And none of the next ten picks after him are players I've ever heard of.
3) The #59, Maxime Dagneault, a goaltender who never made it to the NHL.
4) The #92, Derek Krestanovishwho never got above the ECHL.
The Flyers also received the #85 pick in 2003 as compensation when Oates signed elsewhere.
 Here's a roster based on just the first round draft choices, it could probably contend for gold in Vancouver next month:
Thomas Vanek -------- Ryan Getzlaf ------- Corey Perry
Zach Parise ------------ Eric Staal ------------ Jeff Carter
Andre Kostistyn ------ Mike Richards ----- Dustin Brown
Milan Michalek ------- Ryan Kessler ------- Nathan Horton
 The Flyers acquired entry-level holdout Mike Comrie on December 16, 2003. They signed him and traded him away on February 9, 2004. Here's what those 55 days cost them:
To get Comire:
2001 first round selection Jeff Woywitka
2004 first round pick (#25-Robbie Schremp)
2005 third round pick (#81-Danny Syvret).
In return for Comrie:
What a mess.