What damages doors?

Explosives:

Explosives always destroy any door with a finite strength.

This includes the GEP Gun (both types of rounds), the LAW, and LAMs.

In the environment, you can also find TNT crates and explosive barrels with yellow decals on the side. You can even use TNT crates directly without shooting them: just throw the TNT crate directly at the thing you want to blow up, and duck behind a corner to avoid the blast. (*1)

Barrels with red decals on the side don't seem to work.

Use of any of these explosives will destroy all doors (cabinet doors, chest lids, ...) within the radius of the explosion, even if they are on the far side of a wall.

Sniper Rifle with Master-level Rifle skill

Works on most doors with strength 50% or less.

Not all 50% strength doors will yield to the sniper rifle. There are a bunch of wooden doors in the Paris streets ("Paris - near the Champs-Elysses") that have 50% strength, but can't be broken by the sniper rifle.

Master rifle skill + sniper rifle also works to destroy cameras, turrets, and alarm panels in a single shot. A silenced sniper rifle lets stealth players destroy these security devices with impunity. (Less stealthy players can use Sabot shotgun rounds.)

Dragon's Tooth Sword:

With Master Weapons: Low Tech skill and a L2 Combat Strength augmentation (arm augmentation slot), the Dragon's Tooth Sword can break most doors with 50% strength, as well as cameras, turrets, and alarm panels. Sometimes you can also break 70% strength doors; other times there are 25% doors that resist the Dragon's Tooth.

Breaking cameras, turrets, and alarm panels with the Dragon's Tooth sword is silent.

Other methods that work on weak doors:

Weak doors, with strength 25% or less, can often be broken using:

• Melee weapons - crowbar (6 base damage) or baton (7 base damage). I prefer the baton, because it only takes up one inventory slot.
• Pistol - 14 base damage
• Stealth pistol - 8 base damage
• Mini-crossbow using normal (gray) darts - 25 base damage, and you get the darts back afterwards!

Weak doors include:

• Locker doors in shower blocks and barracks
• Doors of shipping containers
• Rear doors of cargo trucks
• Doors that are mirrors (??) (i.e. upstairs at Smugglers)
• Some wooden doors
• Rarely, these tricks work on strong doors as well. It never hurts to shoot a few mini-crossbow darts at a 50% door, to see if it breaks.

AI exploits:

All NPCs can open all doors - if you can trick them into running through them.

If you attract the attention of a guard by making a loud noise, they will open any doors in-between you and them in order to search for you.

Conversely, if you scare a civilian (or cripple a soldier), they will run away from you. If you get them to run in the correct direction, they will open doors in an attempt to escape from you. For example, if you scare the Australian girls in front of the Lucky Money Club in Hong Kong (try shooting the chairs they are sitting on), they will run past the doors and you can get into the club without paying.

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(*1) I threw a lot of TNT crates directly at things because my last playthrough was a "No pistols, no rifles" playthrough, which means that I didn't have any ranged weapons to shoot a TNT crate with.

• GEP guns work on everything without infinite strength:
• LAM rounds
• Dragon's Tooth Sword works on most wooden objects such as doors (tested up to 50% str)

^{Am I missing something? Please help improve this answer!}