A study* claims that overcharging by 0.01V reduced the life of an Li-Ion accumulator by more than 50%. The conclusion was that by reducing the charging to 80% of the full capacity you can prolong the life of accumulator very significantly (click to enlarge):
If the battery is under 40% charged, higher charge current (when it finally is recharged) will result in more heat, which shortens the life of Li-Ion accumulator. Also, depleting the accumulator has the obvious drawback that you won't be able to use your device when you need it.
Some laptops (like my Lenovo T61) have an option to stop charging the battery when it is 95% full, in order to prevent this overcharging problem and prolong the life of the battery. I wish more devices had this option.
* K. Asakuraa, M. Shimomurab, Т. Shodai, "Study of life evaluation methods for Li-ion batteries for backup applications", Journal of Power Source, 2003, PDF: