I'll offer some predictions for some of the players that stand out. Expect at least half of these players to do exactly the opposite of what I predict.
Kenny Anderson (Unrestricted) - Move on in search of some more PT before he's done.
Vin Baker (Unrestricted) - Move on as he tries to (once again) get his career going again.
Brent Barry (Unrestricted) - Consider offers, but remain in Seattle.
Bruce Bowen (Unrestricted) - Remain in San Antonio.
Kobe Bryant (Unrestricted) - Remain in LA (as a Laker), or leave via a sign-and-trade.
Marcus Camby (Unrestricted) - Remain in Denver.
Keon Clark (Unrestricted) - Move on in search of more PT.
Jamal Crawford (Restricted) - Remain in Chicago, or leave via sign-and-trade if his stock rises.
Marquis Daniels (Restricted) - May attempt to leave, but the Mavs will ultimately match any offer.
Vlade Divac (Unrestricted) - Remain in Sacramento
Marcus Fizer (Restricted) - Leave via sign-and-trade if there's any interest.
Kendall Gill (Unrestricted) - Retire or move on.
Manu Ginobili (Restricted) - Remain in San Antonio
Horace Grant (Unrestricted) - Retire
Tom Gugliotta (Unrestricted) - Remain in Utah
Lindsey Hunter (Unrestricted) - Remain in Detroit
Robert Horry (Unrestricted) - Move on (returning to Houston or LA)
Troy Hudson (Unrestricted) - I'm leaning towards him leaving in search of a starting role/more $$$
Avery Johnson (Unrestricted) - Retire
Toni Kukoc (Unrestricted) - Move on
Karl Malone (Unrestricted) - Retire
Kenyon Martin (Restricted) - Remain in New Jersey
Antonio McDyess (Unrestricted) - Move on
Darius Miles (Restricted) - Remain in Portland
Steve Nash (Unrestricted) - Remain in Dallas
Steve Smith (Unrestricted) - Move on in search of one more shot at being a starter
Rod Strickland (Unrestricted) - Move on or retire
Rasheed Wallace (Unrestricted) - Remain in Detroit
Kevin Willis - Retire
I'm expecting most of the other significant free agents will remain with their current teams, especially those who are restricted free agents. No doubt we'll see a lot of the lesser players moving on.