Crimewatch is a system in EVE Online that monitors crime, informs players about pilots who have recently committed crimes, and imposes restrictions on players who have committed crimes. The Crimewatch system is getting a big update in EVE: Retribution. See CCP Masterplan's devblog post for more details about crimewatch.
The major new feature of Crimewatch is Flags. Individual players can be flagged for certain actions. Such actions may also cause other players to be flagged.
Flags have timers around them to show how long it will take before they go away. You can over over your flags to see the specific amount of time remaining and to get more information about why the flag is there.
A Weapons Flag is placed on a player who uses offensive modules (turrets, missile launchers, ECM and other ewar modules, drones) on another player. This includes activating non-targeted weapons. When you have a weapons flag, you are prevented from jumping, docking, and switching ships in space.
A PVP Flag is placed on a player who uses offensive modules on another player. If the target is a piloted ship, the player in that ship also gets the PVP flag. When flagged with this, your ship will stay in space if you log off.
An NPC Flag is placed on a player who uses offensive modules against an NPC, or on a player who is targeted by an NPC's offensive modules. When flagged with this, your ship will stay in space if you log off.
A legality flag is placed on a player who commits a criminal or suspicious action. There are two such flags: Criminal Flag and Suspect Flag. The nature of the legality flag placed upon you depends on the severity of the act. You can only receive a legality flag in Empire space, but you can't get rid of the flag by going into and out of null.
Getting Other Players' Flags
If you use assistance modules (logistics modules such as sensor boosters, shield transfers, remote armor repair, etc.) on a flagged player, you will inherit all of that player's flags. Your timers will be synced with the flag timers of the combat ships you are assisting.