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

Al, I agree, but when people refer to DF (including this discussion), they mention control of the woofer. The effects of complex load should diminish when source impedance is 10 times smaller than the load. DF=20 should be a good choice. At this point I would prefer output impedance that is constant with frequency over high DF. My amp’s output impedance varies from 0.002ohm@5Hz to about 1ohm@20kHz. Tweeter’s impedance is very high at 20kHz but there usually is some network of resistor in series with capacitor, parallel to the tweeter. Can this affect the sound?

sure! of course! The RLC network is frequency dependent. isn’t that the reason for Zobel networks? The Zobel is for the power amplifier (not the speaker) even tho’ some manuf recommend attaching the Zobel to the speaker’s terminals rather than the amp’s output terminals.

OH MAN AGAIN...

Interesting to hear you Gurus going back and forth...

Need to reread this several times , list those for and against an effect, throw out the high and the low - and then consult the Russian Judge!

And in a some-what related question: I am presently using a Phillips High Fidelity Labratories Pre-Amplifier(1980?) - would the damping factor be affected if I switched to a Line-Level triode preamp (like the Wolze I have)? Does/can the preamp affect the damping factor of a amplifier?

heh! heh! heh! ;-0
And, here you thought you asked an innocent question! ;-) 
Also search the archives for damping factor discussions. There is MUCH written on this topic....
And here's some more dope on the subject for you to read (seems to fall in-line with what Ralph/Atma-sphere was saying that DF of about 20 is sufficient):

http://www.butleraudio.com/damping1.php

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.