Games here are ones where arresting is an active choice made by the player, not where suggested by the plot or cutscenes. Usually, arresting requires catching a fleeing suspect and immobilizing him or her long enough to put the cuffs on him. A bonus is often given to bringing them in alive (such as in Red Dead Redemption).
Examples in Games
In the arcade shooter, players were expected to blow away bad guys. However, if you managed to walk up and stand next to most enemies for about a second, they would throw up their hands and float off screen marked as "busted." Busted enemies contributed to extra points at the end-level tally screen.
Pursuit Force and NARC (2005)
Pursuit Force had third person action sequences where the player could run up and melee an enemy which usually entailed taking handcuffs, putting them on one hand, sliding the other cuff under the enemy's groin and cuffing the other free hand.
Red Dead Redemption
Red Dead had bounty hunter missions where the player would get more money if the bounty was captured alive. This was done by arresting targets, which had to be done by way of tying them up with a lasso.
In L.A. Noire, certain suspects can be arrested during chase sequences. To stop and arrest them, the player must keep their sights on the suspect long enough to trigger firing a shot in the air, which scares the fleeing criminal and results in his surrender and arrest.
Judge Dredd vs Death, and the SWAT series
These games feature a "challenge" key that yells at suspects to "get down!" "drop your weapon!" etc. This affects an invisible level of AI morale that will trigger criminals to surrender if reduced enough. Less-than-lethal weapons (gas grenades, beanbag weapons, etc) are also featured to encourage stubborn perps to submit. You are then required to restrain surrendered criminals with handcuffs.