What is the analog bandwidth of general purpose ADCs?
Disclaimer: the answer below is about definition of the analog input bandwidth (AIB) of an ADC; not the particular value of AIB of a general purpose ADC.  

An input analog signal, before being digitized, on its way between input pins of the ADC chip and a digitizing unit (usually a comparator), is attenuated (due to intentional or parasitic RC circuits present or not enough current to charge capacitors). For instance, signal attenuation may happen due to large input capacitance of sample and hold unit (assuming it is embedded into the ADC chip) or parasitic capacitances of comparators.  The frequency at which the input signal is attenuated by 3 dB is called analog input bandwidth.  

If one sends an input sinewave at the AIB frequency, before being digitized it is attenuated by 30% (which is unlikely acceptable). Thus, it’s preferable that maximum input frequency should be about 1/3 – 1/5 of the AIB. For instance, if AIB=500 MHz and input signal is 100 MHz, attenuation (measured by amplitude) is 2% (vs 30% for an input signal at 500 MHz).  

Below is a chart from the datasheet of ADS54J40 showing how input circuitry attenuates the input signal (as seen from the picture, the AIB is about 1.2 GHz). Also see the discussion on the topic (pages 23 and 24 of the datasheet).  

  

PS: Drop of SNR by 3 dB (equivalent to 0.5 LSB decrease in ENOB) is a consequence of analog input bandwidth limitation, but not definition of it. SNR (and ENOB) are driven by many factors, not only by AIB.  

Useful reading on the topic (paragraph “Bandwidth”).