If you charge up the base, then leave it floating, the base capacitance
must discharge through the base, which takes time. It will be faster if
it discharges through the current-limiting resistor that you may find on
the output of a CMOS logic device, but it'll discharge faster yet if you
put in that resistor to ground.
If your base is sitting there at 0V with lots of capacitance to the
world (or just the wrong conductor) your transistor may turn on from
EMI. The resistor to ground will help prevent this.
If you're running the thing close to it's rated voltage, a resistor from
base to ground will help keep it from leaking excessive collector current.
There are more caveats yet, but these are the biggest ones that I can
It depends on how completely off you need, and how quickly
it has to achieve off.
Any transistor with collector to emitter voltage has some
(possibly very small) current leaking into the base from the
collector. The open base transistor amplifies that leakage
current with its current gain. When a turn on base current
goes to zero, the charge stored in the base can take quite a
while to drain away while the transistor slowly turns off.
This is a Bad Idea. It can make your circuit sensitive to stray charges and
temperature effects. There are several extremely sensitive circuits on the
web that use transistors with floating base.
Never leave inputs floating. Always use the appropriate resistance or
recommended termination method on unused inputs. CMOS is especially
sensitive due to the high input impedance.
Many op amps share internal bias supplies. If you use only one section of a
dual or quad, the other sections can upset the bias supply and make the one
being used behave strangely. To prevent this, tie the postive inputs of
unused sections to the appropriate voltage, and connect the negative inut
to the output pin.
Always check the manufacturer's recommendation on floating and unused
inputs to prevent hours wasted troubleshooting silly problems.