UPDATE
Have included an image. As you can see, LED is ON when base is floating. This is a 2N222A transistor.
Playing with an NPN bipolar transistor. The Collector is connected to the positive terminal of a 9V battery through a 1k Ohm resistor, and the Emitter is connected to the ground through an LED. The Base is not connected to anything.
The LED seems to be dim in the above case. When I connect the Base to the positive terminal, the LED is much brighter. That makes sense as current through the base Base amplifies the current.
My questions is: should any current flow through the emitter if the base is not connected to anything? I.e. Shouldn't the LED be completely off?
I have a similar question for NPN Unijunction transistors (understand that nomenclature changes from CBE to AGC)?
Best Answer
Okay, looking at the picture I think you may have the transistor the wrong way round.
Try turning it round.
See this picture for reference:
As you can see the collector is on the right with the flat part facing you, so you have the collector connected to the LED in your circuit (if the 2N2222A part you are using has the same pinout)
I got the picture from here.
EDIT - It's actually a 2N222A, but the above advice still goes as the pinout appears to be the same from the picture posted.
As Russell mentions the more standard way is to connect the LED to the collector, but your circuit should work if set up correctly.