... how important is Damping factor in determining what amp to buy

Here's a further link:
http://www.dissident-audio.com/Loudspeakers/CriticalLSDamping.pdf

Correction to my previous post:  When I said "solid stage preamp" I meant "solid state power amp."  Not sure how that error occurred.

Regards,
-- Al
 

Important if it is off the rails in one direction or the other but, at normal values, somewhat less important, and....after a point, higher isn’t necessarily better, as others have pointed out.
It is simply a measure of the amplifier’s output impedance, which may be more important with speakers that have impedance variations with frequency, and/or large impedance dips. When you divide the amplifier’s output impedance into the speaker’s input impedance, that is your damping factor. Amp manufacturers often use "8" ohms for the speaker’s input impedance when they calculate their advertised damping factor. This may or may not be accurate, all or some of the time but they have no way of knowing what speakers will be used.
Damping factor is something to be aware of if you are changing out speakers or amps, but not usually a deal-breaker or deal maker.

As the VTL literature explains, achieving higher damping factor/lower output impedance, if done using negative feedback (as is often the case), can come at the cost of reduced sound quality above bass frequencies. A good reason to either bi-amp, or use a sub with a dedicated amp and a separate amp uncompromised by damping factor considerations for the main speakers. That, or chose a speaker not requiring a low output impedance amp to sound as good as it can at both low and higher frequencies.

... and in my on-going search for audio intelligence:
does the age or broken-in-ness of the speaker affect the amps ability to dampen it? (example: right now, my Phillips pre and Onkyo A7 Main-In is powering a vintage pair of JBL L25s...)