The lifetime of the lithium ion batteries can be found in mobile phones, PDAs, UMPCs and notebook computers isn't endless. However, you can make it longer.
The ugly truth
Batteries are chemical labs and even if you use them in perfect condititons and the highest care possible, they will get worn sooner or later. They just loosing the ability to keep their power.
The more times the battery has fully recharged the more the battery get worn. Or you can say the the more time you use your device on battery the earlier the devices battery get worn.
The first charge is important for the battery and your device too. The battery has to be charged long time, 12-16 hours first time to use all the chemicals it has. Some says that the polymer batteries don't need the first big charge but specialist says it's good prctice to do it with the LiPoly batteries too. Note, that you have to wait until the battery reaches it's critical level (around 5%) before start the first big charge. The first charge also calibrates your devices power meter.
Hot and Cold
Both high and cold temperature shorten the lifetime of the battery. In real life the latter happens more often. When you are accessing broadband internet or doing something else that heats up your device, you have to keep in mind that overheated device can overheat the battery too which is very bad.
This applies to mobile devices. Recharging battery while the device is switched off makes recharge time shorter.
If you started to charge a battery try to don't abort the charging process. It can cause inaccurate power level indication and can decrease some batteries lifetime too.
It's a good practice to keep your device on charger when you are actually using it, but not the best practice to keep it on charger when you are not. Better detach or swith off charger when you are not using your device, but only after it is fully charged.