As njd pointed out, most cell phone batteries are Lithium Ion now.
Although constant charging cannot hurt, it looks like you may want to periodically run the battery all the way down so the digital circuits can correctly calibrate:
Although lithium-ion is memory-free in terms of performance deterioration, batteries with fuel gauges exhibit what engineers refer to as “digital memory”. Short discharges with subsequent recharges do not provide the periodic calibration needed to synchronize the fuel gauge with the battery’s state-of-charge. A deliberate full discharge and recharge every 30 charges corrects this problem. Letting the battery run down to the cut-off point in the equipment will do this. If ignored, the fuel gauge will become increasingly less accurate.
As for battery life, temperature is apparently a factor — the hotter the environment, the more capacity loss over time. And storing the battery at 100% charge is actually unhealthy for Lithium Ion batteries!
Great set of Lithium Ion battery use tips here: http://www.batteryuniversity.com/parttwo-34.htm
Avoid frequent full discharges because this puts additional strain on the battery. Several partial discharges with frequent recharges are better for lithium-ion than one deep one. Recharging a partially charged lithium-ion does not cause harm because there is no memory. (In this respect, lithium-ion differs from nickel-based batteries.) Short battery life in a laptop is mainly cause by heat rather than charge / discharge patterns.
Batteries with fuel gauge (laptops) should be calibrated by applying a deliberate full discharge once every 30 charges. Running the pack down in the equipment does this. If ignored, the fuel gauge will become increasingly less accurate and in some cases cut off the device prematurely.
Keep the lithium-ion battery cool. Avoid a hot car. For prolonged storage, keep the battery at a 40% charge level.
Consider removing the battery from a laptop when running on fixed power. (Some laptop manufacturers are concerned about dust and moisture accumulating inside the battery casing.)
Avoid purchasing spare lithium-ion batteries for later use. Observe manufacturing dates. Do not buy old stock, even if sold at clearance prices.
If you have a spare lithium-ion battery, use one to the fullest and keep the other cool by placing it in the refrigerator. Do not freeze the battery. For best results, store the battery at 40% state-of-charge.
Modern cell-phones all use lithium-ion batteries, which work best with frequent top-up charges.
They have circuitry to monitor the input voltage and prevent over-charging.
Some chargers get quite warm while connected to the mains supply, and that’s just wasted energy; so you might want to disconnect the charger from the mains once your cellphone is fully charged, but there will be no damage to the battery if you leave it charging a few hours longer.
All devices should stop charging once they’re full. However, they might start recharging when the charge drops down to 80-90% depending on the manufacturer.
If I’m rights most batteries should be rated for about 1000 charge cycles before serious degradation occurs. If you charge the phone at night, in the car and at work that would be about one year. After that you might as well buy another battery since they are getting really cheap. Just dispose of the battery environment friendly.