You're right in that when your digital signal "clips" at 0dB, it's an absolute maximum limit. 16-bit audio has 2^16 possible volume levels, and once you get to 2^16, there's no higher number to express your sound, so it maxes out, or clips.
With analog signals, your "clipping" limit is less well defined. The term distortion in an amplifier just refers to non-linear response, (and it so happens that's when you get your nasty harmonics and crackle). So distortion is harder to define when it becomes unacceptable and destroys the sound for a listener.
To look at why distortion happens, let's take a look at amplifiers. A perfect amplifier takes in a signal, and multiplies it by a constant factor. In theory if you chain a load of perfect amplifiers together, you could get unlimited volume. However, real amplifiers need to get their power from somewhere...
Your limitation is the voltage of the power supply on the amplifier - if your amplifier circuit is powered by 10V, it will amplify a 0.1V signal to a 5V signal happily, but as your signal gets near 10V, it will start to distort, up until the point where it reaches 10V and you loose all your signal's information. The graph below approximates an amplifier's response. For small voltage inputs (x near 0) you have a diagonal line, so the output (y) is linear, directly proportional to the input. As X gets big though, the graph flattens out as the amplifier reaches its supply limit, so you reach a maximum output Y, and hear distortion.
Expensive amplifiers have a more linear response, and are less prone to distortion, but your "ceiling" is the maxiumum voltage across the amplifier, or the maximum current it can draw.