I'd hate to say it, but one of the best teams that draft is the New England Patriots. They always get value for their picks, and their scouting department is phenomenal. After the 2000 draft in which they got Brady, Theyve Picked the following starters
2001 Richard Seymour and Matt Light
2002 Daniel Graham and Deion Branch
2003 Ty Warren, Eugene Wilson, Asante Samuel, Dan Koppen
2004 Vince Wilfork and Ben Watson
2005 Logan Mankins, Ellis Hobbs, and Nick Kaczur
2006 Laurence Maroney, Chad Jackson, David Thomas and Stephen Gostkowski
Their Drafts get better over the years and all of these guys have contributed to the Pats success over the years, a good front office is the key to success in this league. Their mid-round picks such as Samuel, Light and Kaczur shows that the way to build a succesful team is in the 2nd, 3rd, 4th rounds. And while they have lost some guys like graham and branch, they got a 1st rounder in return this year for deion. Unfortunately I don't see their draft luck running out anytime soon.
Now on the other side of the coin I would have to put two teams The Detroit Lions, for obvious reasons and the Washington Redskins. Daniel Snyder still has yet to grasp that you actually need to build through the draft. In 2003 and 2004 combined they only had 7 draft picks, and only one first rounder (Sean Taylor). They only have four picks this year and after the 1st round, they dont have one until the fifth. This is one of the main reasons why I do not feel the redskins have been at all succesful in the past several years, with the exception of 2 seasons ago.