Often there will still be a resistor placed between the emitter and ground in a CE amplifier.
It's referred to as a degenerative resistor, and helps to provide bias stability to the amplifier. It's a form of negative feedback that helps to limit dependence on the specific beta values (which vary dramatically from device to device)
Often, you may notice that this resistor is significantly smaller, and the output for a CE amplifier will always be above the collector.
Another common disconnect from ground that you may see is a capacitor. This is often used to counteract the negative effects of biasing the device by providing something close to a short to ground at high frequencies.
One way to think about the type of amplifier is to look at which terminal the signal doesn't pass through. In a CE amplifier, it goes into the base and out the collector. In a CB amplifier, it goes into the emitter and out the collector. In a CC amplifier, it goes into the base and out the emitter.