The biggest need for the Patriots hands down has to be the need for a pass rush. Never getting to the quarterback (besides Tully Banta-Cain's impressive sack record...but that happens when you are the only one sacking) made the secondary look even more horrid than it may have been...let's see if there are any options out there.
Since I assume that next year will wind up being an uncapped year, any free agent who hasn't been in the league for 6 years will lose his free agency status, meaning they will become restricted free agents...and most restricted free agents don't leave. So I'll do my best to make sure who is and isn't restricted and unrestricted now, but please correct me if i am wrong.
Elvis Dumervil, Denver Broncos (would be restricted) - 4 seasons with the Broncos, registered 42 and a half sacks, including 17 last year...also had 4 forced fumbles. A true pass rushing outside linebacker, exactly what the Patriots need, and we'll most likely never get a shot at him. Made $535,000 last year, but expecting a hefty payraise.
James Harrison, Pittsburgh Steelers (unrestricted) - I don't know why he's not being brought up more, so I may be wrong about his free agency status. But according to KFFL he is a free agent, and even with an uncapped year he'd fit the 6 year bill. Has registered 38 and a half sacks in his six seasons, including 10 this year, and 16 in 2008. Made $800,000 last year, but had a 10 million dollar signing bonus.
Chike Okeafor, Arizona Cardinals (unrestricted) - 10 seasons with 3 different teams. 53 career sacks, including 4 and a half each of the last two seasons. Past his prime, but a definite upgrade over what we have (Burgess). Made 4.5 million each of the last three seasons, but the number is expected to drop down a bit.
Aaron Kampman, Green Bay Packers (unrestricted) - 8 seasons with Green Bay, 54 sacks. Career high 15 and a half in 2006. Partially tore his ACL in November, but is expected to be fully ready for training camp. Green Bay may not re-sign him due to the injury, and he may be worth the risk. Made 3.9 million, but that number may fall back down to 2-3 considering the injury.
A few defensive ends are available as well.
Adewale Ogunleye, Chicago Bears (unrestricted) - 9 seasons, 67 total sacks...but has only played all 16 games in 4 of those seasons. Has forced 15 fumbles in his careers, as well as recording 2 safeties. Made 4.8 million, and not sure whether that number will drop or rise.
Jason Taylor, Miami Dolphins (unrestricted) - Recorded 7 sacks in his return to the Dolphins this year, after a poor season with the Redskins. In 13 NFL seasons, Taylor has recorded 127 and a half sacks and forced 44 fumbles. Seems to have lost another step or two, but only made $845,000, a substantial pay cut from years prior.
Kyle Vanden Bosch, Tennessee Titans (unrestricted) - 42 and a half sacks in 9 seasons, and only recorded 3 sacks last season. Salary has hovered between 3 and 4 million the last couple seasons, and isn't expected to lower much more than that.
If you want any other mini-bios, feel free to let me know and I will inlude them. Here is a list of some lesser-tier players that may also have an impact.