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.
Master sniper rifle:
Works on most (but not all) doors with strength 50% or less. It also works to destroy cameras, turrets, and alarm panels, which is a superb way for stealthy players to knock out automatic security.
Note that 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 opened by shooting them with the sniper rifle.
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.
Other methods that work on weak doors:
Doors with strength 25% or less can often be broken using melee weapons or pistols. Rarely, stronger doors can be broken this way too.
The mini-crossbow using regular darts (the ones that come in gray boxes) is a good candidate because it deals high damage, and the darts are not consumed when they hit a door. A 25% locker door is generally broken in two hits, and you get the darts back afterwards.
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.
(*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.