Question: I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.

Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the same? The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?

[Edit]
All answers explained a bit of everything, so it was hard to choose one. If YOU are looking for an answer, please check the others too, in case the accepted one doesn't answer your question.

Answer: 
The circuit in its whole will settle into an equilibrium state.
If you were to shoot a very short pulse of electrons through your lamp, then indeed, the current would decrease right after the lamp.

But if you have a constant flow, then, as another user illustrated, you'd have electrons bunch up right before the lamp, which limits the output, but ALSO the input! The "traffic jam" works its way backwards, all the way to the source, and eventually slows down all electrons from source to lamp.
There's a lot of overly complicated answers here. I will keep it as simple as possible, and try to address your points.
Current is the movement of Electrons. Protons don't move.
A power supply does not "produce current" as such. Current is caused by Voltage (which is a difference in electrical potential.)
The best analogy is water pressure. Voltage is the water pressure, the resistor is your tap or faucet, current is the flow of water. If your tap is partially on and left constant, then the flow of water is determined by the "Voltage". The higher the water pressure, the higher the flow. Alternatively, with the pressure constant, you can vary the "resistance" with the tap. Open the tap more = lower resistance = higher water flow.
So the formula is Current = Voltage/Resistance.

There can be some confusion when we talk about a circuit being a "10Amp Circuit" but that is the maximum current, not a constant.

Lets consider a simple example using a Car Battery, which is typically referred to as 12 Volts. (Its actually closer to 13, but we like even numbers)
It is always at 12V, even with no current flowing. Once a circuit is completed, current begins to flow. For the purposes of discussion we can ignore the resistance of the wires and focus on the light bulbs. Something like a brake-light would have resistance of about 12ohms so the current for one light would be around 1amps.
Whereas a headlight has lower resistance, around 3ohms, so the current would be around 4amps.
That's the tricky part to understand. A brighter, more powerful light, actually has LOWER resistance.
Again, I'll go back to the water example, only lets make the water hot, and say you're trying to heat something up by running hot water over it. The faster the water, the more heat is put into it.

Hope that helps