Frequency-dependent behaviour of opamps
The open-loop gain looks more-or-less like a large gain followed by a simple (first order) RC low pass filter (only one R and one C) with a pole typically at around 10Hz to a few kHz- fc. 

So at much above fc, the gain falls off at 20dB/decade. 



For a real op-amp the gain might be 120dB at &lt;&lt; fc and drop to 0dB at 10MHz. 



Another way of saying this, as @Ignacio commented, is that the product of gain and bandwidth is constant (at much above fc, that is, for DC the gain does not go to infinity). This product is called GBW (gain multiplied by bandwidth). 

You can see the deviation from -90° phase in the real op-amp phase response. Above a few MHz other stages in the op-amp begin to have an effect. The phase shift is still far from -180° when the gain drops below 1 (0dB), which means that this op-amp is unity-gain stable.