Regular alkaline batteries are not designed for recharging --- although there are rechargeable alkaline manganese (RAM) batteries on the market, but reports about them are poor and it's understood they can only be recharged about 20 to 30 times. There are a few things that can happen if you decide to put a regular alkaline battery into a charger, so caution needs to be exercised.
Alkaline Battery Chemistry
In chemical terms, alkaline is at the opposite end of the pH scale, pH meaning "potential hydrogen." The opposite end of the scale from alkaline is acid, so an alkaline doesn't contain acid. Despite its name, an alkaline battery is most often made from zinc chloride or carbon zinc. The reason they are generally referred to as alkaline batteries is because the chemical mix has been altered to make it more alkaline. This chemical make-up means that they are generally unsuitable for recharging.
Nickel Battery Charger
Never put your alkaline batteries into a charger designed for nickel-based batteries. The charge rate is excessive and there's no safety cut-off, so left unattended, the charger would continue to try to charge the alkaline battery, causing excessive heat and a risk of fire.
Lithium Battery Charger
Lithium battery chargers are designed to charge at a very high rate, about 4 volts, which is two and a half times the voltage from an alkaline battery. They also charge fast, so if you put an alkaline battery into a lithium battery charger, expect it to heat up rapidly, then catch fire; it may even explode. You're also likely to damage the charger beyond repair.
Purpose-Made Alkaline Charger
Although not that common, there are chargers designed to recharge an alkaline battery. You need to recharge the battery before it's totally discharged, otherwise it won't recharge. The charge rate is very slow, so it takes some time, but you do get to save money in the process.