ANY battery can, in principle, be recharged. Whether you want to try it depends mainly on your tolerance for rather nasty results.
In any battery, a chemical reaction of some sort produces a voltage. When current flows out of the battery, the continued chemical reaction maintains the voltage.
By applying a higher voltage to the battery terminals, you can make the chemical reaction "run backwards" so that whatever gets "eaten up" by the normal action is - at least partially - restored.
In most disposable primary cells, the casing for the cell is partially consumed during discharge. While recharging may partially restore the (usually metal) casing, there is no guarantee that it will be restored evenly, and even a few discharge/charge cycles will usually result in a case rupture which will leak very nasty stuff all over your fine electronic equipment.
In addition, most of the common chemical processes tend to produce gasses. Since non-rechargeable batteris are usually not vented, there is the very real possibility of an "explosion."
Batteries intended for recharging are made either with a casing so thick that it is expected to outlast any reasonable number of charge cycles, or have a separate - nonreacting - case. Some rechargeables are also vented. Common disposables have none of these features.
Even with batteries designed for recharging, there are some hazards. At least two series of Compaq portable/laptop computers, and one Apple series have been recalled because of "frequent" Lithium Battery fires/explosions. (Note that this was a battery mfg problem, and is not meant to reflect on the quality of the computers. Information is not "publicly" available on any similar problems other mfrs may have had.)
You can, in fact, "recharge" ordinary carbon/zinc and other batteries, and devices to do so have appeared occasionaly in the marketplace. The likelihood that you will destroy the equipment in which the recharged batteries are used makes it a rather dubious saving.
Recharge disposable batteries (carefully) if you want, but use them only in "disposable" equipment.