How fast will an op amp respond to changes in input voltage?
The parameter you want is the Total Response Time:


  The time between a step-function change of the input signal
  and the instant at which the magnitude of the output signal
  reaches, for the last time, a specified level range (±e)
  containing the final output signal level.


This definition is from Understand Operational Amplifier SpeciFfications by Jim Karki.

Another parameter that might be helpful is the phase shift through the amplifier. For signal frequencies where the open loop gain is unity this is specified as the phase margin.

Note that the output slew rate parameter is something else altogether. The slew rate of an amplifier indicates the ability of the output stage to make large voltage changes, rather than the delay from input to output.