If you set a battery on a concrete floor it will discharge.
This was true when batteries were manufactured with hard rubber or tar casings. Over time, those materials could develop microcracks, making the casing porous. As a result, placing the battery on a conductive surface could cause it to discharge. However, with modern plastic casings, this is no longer a concern.
Fully discharging a battery will extend it’s life
Battery memory was a significant issue with NiCad batteries. NiMH batteries experience this effect to a much lesser degree, and it can usually be corrected by running the battery through a complete charge and discharge cycle. However, many other battery types can be damaged if they are fully drained to zero. Because each battery chemistry behaves differently, it is important to follow the proper care guidelines for the specific type of battery.
Overcharging a battery can damage it
This is partially true. Most electronic devices can be damaged by excessive heat. Continuing to supply current to a battery after it is fully charged may cause it to overheat, potentially cracking the casing or drying out the electrolyte. However, warnings about charging a cell phone overnight are often overstated. Many modern electronic devices are equipped with charge controllers that reduce current when the battery becomes too warm and stop charging once it reaches full capacity. As a result, overnight charging is generally not a significant concern for most modern devices.
Brand X batteries last longer
In general, alkaline batteries last longer than carbon-zinc batteries, and larger batteries typically provide more runtime than smaller ones. However, battery capacity is determined through standardized testing, not informal comparisons using toy rabbits or flashlights. Manufacturers often publish specification sheets that list capacity in milliamp-hours (mAh). Unfortunately, finding results from controlled, unbiased tests can be difficult, especially when they are buried among marketing claims.