What do you look for in damping factor?

anything close to a 100 is good, above this you are unlikely to gain significant audible improvements (diminishing returns)

There are many answers to this seemingly simple question! There are some that say that a low number is just fine - I think that I read on the Gamut website that 25 is sufficient. http://www.gamutaudio.com/faq/details.asp?id=16

There are others that say, a large number is a must - the higher the better - several s.s. amps claim very high damping factors such as 500 or 800 or even 1000.

There are still others that say that DF is a complicated matter & that there is no correct answer that'll satisfy everyone. Since DF is defined as speaker impedance divided by amplifier output impedance & since speaker impedance varies with frequency, DF will also be a function of frequency. In fact, several amplifier's output impedance is also a (different) function of frequency. So, you have a ratio that has both numerator & denominator with 2 totally different functions of frequency. So, the DF curve, is at best, not drawable on a piece of paper when it comes to a real-world operating condition i.e. a particular amp driving a particular speaker UNLESS you know the exact impedance vs. frequency response of both items.
If you do, you have 1 more hurdle - what is the impedance vs. frequency response of your speaker cables? This fellow features in the mix too!

usually, a DF number is spec'd in the manual using 8 Ohms speaker input impedance. However, are any of your speakers 8 Ohms input? If they are, do you really think that they maintain 8 Ohms from 20Hz to 20KHz? what if your speakers are 6 Ohms input? then, is the DF spec'd in the manual any use to you?

So, best is to use your ears to judge if the amp connected to your speakers is providing you the bass response you are looking for. Forget chasing this spec - I believe that it has little info to offer you.
FWIW.

I never purchase on specs including damping factor, just sound quality. But I do know the higher the number for damping factor, the better the amp can control the low frequency drivers. A high damping factor no doubt would result in a tighter more controlled bass and would be an important spec for someone that is considering an amp to drive a subwoofer.

Damping factor is just part of the overall gestalt of a sound system. I used to look at it in isolation, and assume higher is better. But high damping factor usually calls for large amounts of global negative feedback, which introduce high-order harmonic distortion, which has been shown to be pschoacoustically detrimental even in very small amounts. Low damping factor is typically associated with little or no global negative feedback and relatively high total harmonic distortion specs, but that tends to be benign distortion that the ear is very forgiving of. In fact, one of the leading researchers in the field of distortion perception told me that there's a negative correlation between harmonic distortion and subjective preference - meaning that we tend to prefer higher distortion amplifiers, because they tend to have a more psychoacoustically benign distortion characteristic.

So high damping factor can imply sonic trade-offs in other areas.

Some speakers (typically high efficiency speakers) work best with a low damping factor amplifier. Some work best with a high damping factor amplifier.

What happens is, with a very low damping factor amplifier, the frequency response is modulated by the speaker's impedance curve. Almost always this is detrimental. However, a few designers (Silverline comes to mind) use this to give their speakers a smoother frequency response when used with low damping factor amplifiers. The ideal would probably be an ultrasmooth impedance curve, so that there are no impedance bumps to modulate the frequency response.

Now if a speaker has impedance peaks in the bass region, a low damping factor amplifier will often deliver more power into those impedance peaks, making them louder. So the designer can use the bass impedance peak/amplifier damping factor interaction to warm up the bass a bit in what might otherwise be a bass-shy design. That's one reason why high efficiency speakers sound often better on SET and OTL tube amps - such amps will deliver a little extra juice in the bass region where the impedance is high.

In my own designs, I worked very hard to get a smooth impedance curve from about 80 Hz on up, so the speakers should work well with a wide variety of amps. I allowed the bass impedance to peak pretty high so that a low damping factor amp would give me some free bass extension. The port tuning can be varied - I tune it higher for high damping factor amps. I mention this to show how a speaker designer might take amplifier damping factor into account.

Most of the speakers you list work best with medium (20-80) to high (80+) damping factor amplifiers. The Maggies are an exception - while they have a low impedance, their impedance curves are amazingly smooth, so they will work well with low feedback, fairly low damping factor amplifiers. Unfortunately, they also like a lot of power - which is rare in a low feedback amp.

If you were starting from scratch, I'd suggest taking a wholistic approach - choosing speakers from among those models that will work well with the type of amplifier you like, and then making your final amplifier choice.

Duke