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: 
Ok , so I think that confusion lies in the concept of current. When we apply potential difference through a circuit having resistance, a single electron does not move from one end to the other. What actually happens is that it replaces electron next to it which in turn replaces the electron next to it and this happens till the last electron reaches the other terminal. The resistance from beginning itself shows its effect on the movement of charge and not when the charge passes through it. What u say is that a charge when passing through a resistance should lose energy and hence current shoould slow down is partially correct. Yes, resistance does slow down the movement of electron but that effect is observed in overall circuit and not just in the path where resistance is connected.
Here is why the current stays the same going through the bulb:

Think of current as water flowing downstream in a river. The water comes to a dam, and flows over the top, and then falls all the way down to the bottom of the dam, then resumes flowing downstream. Every gallon of water that was flowing in the river will go over the top of the dam. Every gallon of water that flows over the top will fall to the bottom. Every gallon that falls to the bottom resumes flowing downstream. Therefore, every single gallon of water that was originally flowing downstream before coming to the dam will wind up flowing downstream again after leaving the dam behind.

We say that water is *conserved*. One gallon in, one gallon out. Current through a circuit behaves the same way: One ampere in, one ampere out.