I normally plug my BB into my charger when I go to sleep at night and unplug it in the morning when I wake up. There was a tag on the charger to my new 9600 saying remove when finished charging. Is there any harm in leaving the charger plugged into the BB overnight?

AFAIK, you can't damage the device/battery by leaving it plugged in. Lithium-ion batteries aren't like the old Ni-Cads. In fact from what I have been told, it is a good idea to keep them topped up and not run them dry.

I keep my BB plugged into the PC when I am in the office. So far no harm done and I have been doing that for years.

Wirelessly posted

Jim, I do exactly what you do, and I've been doing it since 2006 and I've never had a battery problem.

The battery will never take more charge that it needs, its just not possible. Once its full then it will stop taking charge and that's that. So I don't think you need to worry.

Wirelessly posted (AT&T 8100 Pearl)

You'll notice the charging bolt disappears when it's topped off.

What charging bolt? All I see when my charger is plugged in is a clock.

The Department of Transportation last week released a safety advisory warning of the potential dangers involved with lithium batteries onboard commercial passenger and cargo aircraft. This may be the reason for the admonition on cell phone chargers to disconnect the charger when the battery is fully charged. (I still do not understand how to tell when the battery is fully charged without disconnecting the charger.)

This is part of the DOT safety advisory:
Lithium batteries are deemed hazardous materials because they include both chemical and electrical hazards, the advisory said. If improperly packaged, stored or overcharged, the batteries can overheat and ignite.

The entire advisory is as follows:
SAFETY ADVISORY WARNS OF LITHIUM BATTERY TRANSPORT – The Department of Transportation last week released a safety advisory warning of the potential dangers involved with lithium batteries onboard commercial passenger and cargo aircraft.
The advisory, issued by the Pipeline and Hazardous Materials Safety Administration (PHMSA), in coordination with FAA, discusses recent incidents involving lithium batteries on aircraft and regulatory requirements for their transport in commercial and cargo service.
“PHMSA and FAA are concerned that many persons who ship lithium batteries do not recognize the hazards posed by these batteries during transportation,” the advisory said, adding that some 40 aircraft incidents have involved lithium batteries since 1991. The incidents occurred both before loading the batteries onboard aircraft, as well as while they were transported by air. “Many of the incidents were directly related to a lack of awareness of the required safety measures applicable to shipments of lithium batteries or because passengers failed to follow preventative measures to protect batteries from short circuit or damage,” the advisory said.
The advisory outlined several specific cases, including a Sept. 9 incident in which a passenger flight declared an emergency after a personal electronic device was dropped and the battery pack sparked and began smoking. On Aug. 14, a flight crew received a warning indicating smoke in the forward cargo compartment.
The indication came after the crew had landed the plane. The initial investigation suggested that the fire originated with a shipment of about 1,000 e-cigarettes, each containing a lithium metal battery. The advisory noted that the shipment contained no markings or labels indicating the materials posed a specific hazard or contained lithium batteries.
Lithium batteries are deemed hazardous materials because they include both chemical and electrical hazards, the advisory said. If improperly packaged, stored or overcharged, the batteries can overheat and ignite, the advisory warns, adding this could lead to thermal runaway.
DOT has undertaken several public outreach efforts to ensure compliance with safety handling practices. “Despite these outreach efforts, aviation incidents involving lithium batteries continue to occur,” the advisory said, citing as an example a July 15 shipment containing several thousand lithium ion cell phone batteries loosely placed into fiberboard packages, with no protection from short circuits and no package markings indicating the presence of lithium batteries. One of the packages was found to be emitting smoke after the aircraft landed at its destination.
The advisory states the intention of the agencies to step up enforcement of safety standards. The agencies will be watching for undeclared shipments and stated their intention of bringing enforcement action against illegal transport. “This advisory puts all shippers on notice that noncompliance with the safety regulations is not acceptable,” Transportation Secretary Ray LaHood said. “I have asked the department’s enforcement personnel to increase their inspections and step up enforcement where necessary.”

That is OLD news. Been around for over a year or more. Came about due a laptop battery manufacturer's recall of a certain set of batteries for SONY and Toshiba laptops. AFAIK, it didn't amount to much more than replacing the battery with a new one.

The battery in your device is properly manufactured, packaged and stored. And when it is fully charged the device is smart enough to know it and not keep charging even though it is plugged in.