Battery Guide
Recommended - rechargeable
If you want to recharge your batteries, use Nickel-Metal Hydride (NiMH). These replace obsolete NiCad rechargeable. NiMH's have much higher capacity than NiCd's and don't suffer from memory effect. NiMH's are great all-around batteries but they have a high self-discharge rate (they go dead after a few months even if you don't use them) so they're not good for things like emergency flashlights or smoke detectors.
Recommended - standard
Alkaline: If you don't use many batteries and don't want to get a recharger, then just buy alkaline batteries. They're inexpensive and give plenty of power. If you buy batteries more often than once a month or two, you should probably consider rechargeable instead.
Not Recommended
NiCad's are obsolete rechargeable. They've been replaced by NiMH's which last longer, don't suffer from the memory effect, and aren't toxic.
Rechargeable Alkaline can't be recharged nearly as many times as real rechargeable batteries (like NiMH & NiCad). They also can't be used in high-drain devices like digital cameras, and their capacity drops every time they're charged. But they're good if you need a rechargeable that puts out more voltage than an NiMH.
Heavy Duty, General Purpose. These are Zinc Chloride and Carbon Zinc, respectively. "Heavy Duty" is a big misnomer; these are really "puny duty". General Purpose are very susceptible to leaking.
Lithium batteries are the most powerful batteries you can get, but they're expensive, you can't recharge them, and they're toxic so you can't just throw them in the trash. (You're supposed to take them to your community's hazardous waste facility.) They're great for devices that use the 9V size, since they'll last a long time (10 years in smoke detectors), but for other sizes NiMH is a better bet.
Source: Michael Bluejay's Battery Guide
Battery Guide
Recommended - rechargeable
If you want to recharge your batteries, use Nickel-Metal Hydride (NiMH). These replace obsolete NiCad rechargeable. NiMH's have much higher capacity than NiCd's and don't suffer from memory effect. NiMH's are great all-around batteries but they have a high self-discharge rate (they go dead after a few months even if you don't use them) so they're not good for things like emergency flashlights or smoke detectors.
Recommended - standard
Alkaline: If you don't use many batteries and don't want to get a recharger, then just buy alkaline batteries. They're inexpensive and give plenty of power. If you buy batteries more often than once a month or two, you should probably consider rechargeable instead.
Not Recommended
NiCad's are obsolete rechargeable. They've been replaced by NiMH's which last longer, don't suffer from the memory effect, and aren't toxic.
Rechargeable Alkaline can't be recharged nearly as many times as real rechargeable batteries (like NiMH & NiCad). They also can't be used in high-drain devices like digital cameras, and their capacity drops every time they're charged. But they're good if you need a rechargeable that puts out more voltage than an NiMH.
Heavy Duty, General Purpose. These are Zinc Chloride and Carbon Zinc, respectively. "Heavy Duty" is a big misnomer; these are really "puny duty". General Purpose are very susceptible to leaking.
Lithium batteries are the most powerful batteries you can get, but they're expensive, you can't recharge them, and they're toxic so you can't just throw them in the trash. (You're supposed to take them to your community's hazardous waste facility.) They're great for devices that use the 9V size, since they'll last a long time (10 years in smoke detectors), but for other sizes NiMH is a better bet.
Source: Michael Bluejay's Battery Guide