For
cobalt lithium ion. Lithium polymer cells have most of the same issues (except discharge rate) as cobalt lithium ion.
Other lithium chemistries (LiMn, Li3PO4, LiFePO4) are different.
* Permanent changes after a long time spent unused but fully charged
Cobalt lithium ion gradually loses capacity over time. This is due to an oxidixing effect inside the cell and happens whether or not you use the cell or not. The capacity loss over time is worst at high temperatures, fully charged. It is lowest at 40-50% capacity, a few degrees below freezing
* Temporary changes after a long time spent unused but initially fully charged
Cobalt lithium ion lose charge (self-discharge) very slowly when stored unused but fully charged. Self-discharge is worst at higher temperatures and ranges between 5-10% per month depending on chemistry and temperature.
* Permanent changes after any length of time spent partially charged
As mentioned above, cobalt lithium ion always loses capacity over time due to oxidation. Leaving the cell partially discharged is better than leaving it fully charged.
* Permanent changes after many recharges from a significantly-discharged state
This is the preferred usage model for cobalt lithium ion. You don't want to fully charge them because the oxidation loss is greatest at the fully charged state. Longest calendar and cycle life appears to be seen when running between a 40% DoD and 60% DoD state. But I don't have a lot of research to quote to back me up on this - although a couple of books seem to indicate that this is the case.
* Permanent changes after many recharges from a slightly-discharged state
You generally want to be less charged than merely "slightly discharged" to avoid capacity losses due to oxidation.
* Any changes (permanent or temporary) in response to non-fatal temperature highs or lows (does it suffer at 40 degrees Celsius? 0 degrees?)
Cobalt lithium ion loses capacity temperarily at very low temperatures, and loses capacity permanently at very high tempatures. Significant temporary capacity loss is seen below 40F/5Celsius.
* Does it suffer from rapid discharge?
Generally cobalt lithium ion do not like rapid discharge at all. Most manufacturers spec the cells at 1-2C max discharge, with the typical being 1.5C. Exceeding this increases heat in the cell which reduces the operational life of the cells.
* Does it suffer from rapid recharge?
Generally cobalt lithium ion do not like rapid charging at all. Most manufacturers spec the cells at 1C max charge rate. Exceeding 0.5C charge rate reduces the operational life of the cells. In fact, a really low charge rate can significantly extend the operational life of the cells.
Other things to avoid with cobalt lithium ion cells to extend the operational life of the cells that weren't mentioned above:
Don't charge at, below, or near freezing - you can permanently damage the cells.
Don't discharge the cells below 3V per cell - you can permanently damage the cells.
Data to back up what I wrote above:
http://en.wikipedia.org/wiki/Lithium_ion_battery
http://www.batteryuniversity.com/partone-5A.htm
http://www.batteryuniversity.com/partone-19.htm