What you want with any common emitter amplifier is for the collector DC voltage to be about half the supply voltage. This means that when you have an AC signal present at the input, the amplifier's output doesn't clip the signal asymmetrically.
To achieve this, you need to create a situation where the DC collector current is held fairly constant. So, if Vcc is (say) 12 volts and Rc is (say) 2200 Ω then you want the quiescent current through Rc to be about 2.73 mA. And, 2.73 mA through a 2k2 resistor drops 6.006 volts.
To ensure 2.73 mA flows through Rc means using an emitter resistor. So, if the emitter resistor is 220 Ω (for instance), 2.73 mA flowing from collector into the emitter and then through the resistor would drop about 0.601 volts across it.
It then follows that the base bias voltage would need to be about 0.601 volts plus about 0.7 volts (internal base-emitter volt-drop). This then allows you to calculate the base bias resistors.
So, that's the normal case when an emitter resistor is used.
If you didn't have an emitter resistor, how can you properly define the current flowing in the emitter (and the collector)? Well, you can if you know the maths surrounding a CE configuration but, then you'll find that temperature effects will be surprisingly high and the desired 6 volts at the collector may drift with temperature a few volts this way and that way.
So, do you want a sh1tty circuit that drifts around or, do you want a stable circuit?