Speakers that are very accurate sounding but don't produce an emotional connection.

Shadorne- Assuming you refer to only excellent recordings, I agree that greater performance overall will come via accurate equipment setup correctly in an adequate room. That's been my experience anyhow, and yet I can't ignore that sometimes a louder and more forward instrument can be quite captivating and therefore more emotionally moving. 

It's possible that one can have extremely broad musical tastes, but still prefer some recordings over others not because of how faithfully they're reproduced but because they want to get that emotionally moving fix over and over again. Hey, I like me a mean sax which can be heard in countless genres of music. If I was a sax addict, I would probably be more likely to go in the direction of what pleases me most: more sax!

Thank god I don't have that problem!

For sure more color is attention grabbing just like a speaker with boosted bass and treble can seem wonderful in a short audition and particularly with certain tracks like Daft Punk. Over the years though, an accurate response will better portray your entire collection and lead to greater enjoyment. 

Think of of it like a partner - for the long haul, do you choose the sexy crazy insane person that is exciting and full of surprises but proves totally unreliable in many situations or a balanced person who is solid and just right in all the important ways both inside and out. 

As with all audio 'chat', it may be interesting, but trying to explain your nervous system, and how it 'sums up' to your perceptions, is kind of folly.  But, in the spirit of audio chat, my recent drastic improvement in my system, to the point where I am extremely content, involved replacing the capacitors in the crossover, which were middle of the road, with Jantzen Audio Superior-Z Caps.  It cost me $500, but it was the last chink in what should be an exceptional 'Horn' system, composed of Volti Audio, McIntosh Mc-30s, McIntosh MEN-220, and MCD-500.  I absolutely love my electronics, but without the 'best' Caps prior to the drivers, there simply is not the possibility of getting 'there'.  Of course, I could spend $1500 on the Caps, and purchase the best Mundorf, but for me, I have reached my level of saturated contentment......and the rest, for me, is folly. :)

But, my feelings might be a bit different, if it were possible to actually hear some of the speakers that have my attention, such as Harbeth or Devore 0/96.  Being that this is such an expensive hobby/passion, I ain't laying down the money to purchase, and then being 'stuck' with the item.  I have sold, and lost a bunch of money, on used speakers.  It becomes even more of a pain when no one is purchasing audio for realistic prices, or at least what I see as realistic.  

I have listened to a few speakers over the years that impressed me with their accuracy and presentation of the music, but just did not create an emotional response or connection.

Sunnyjim, I'm not sure I follow what you are saying here (maybe i do but i'm not sure that your & mine audio language is the same...) - usually the most accurate system is the most satisfying system as it portrays the program material with emotion & connects the listener to the music. But...... your statement above says just the opposite.
So, i'm pretty sure that what you think you heard as "accurate" was merely distortion masquerading as accuracy. The distortion was obviously coming from various places incl the speaker - you already know this: one can have the best low-distortion electronics & sub-standard speakers & you will get mediocre playback. The other way is also true - sub-standard electronics & the lowest distortion speakers will yield mediocre playback.

I have often wondered what that quality is in some speakers that produce an emotional connection with the listener.

Many of the readers here will not agree with what I'm going to write (one of them being melbguy1 who's had several arguments about this) but so be it. I'm not trying to convert anyone - to each his own - but I'm quite sure that this is one of the main aspects involved in preventing an emotional connection to the music. I've written this before & I'll say it again - the speaker must be a time-coherent speaker. Time-coherent speakers are the least distorting speakers & they happen to use a 1st-order x-over. Just the physics of the 1st-order x-over ensures that the phase relationship of the music between any 2 frequencies remains unchanged above, at & below the x-over point. No other order of x-over guarantees this. It is extremely important to retain the phase relationship of the music as it passes thru each stage of the music play-back chain. While electronics do distort the program material, the worst offender is the loud speaker. Like I wrote, I've been saying this for a while & atleast a couple of well-known Audiogoners have paid attention to this & they have improved their resp. systems several orders of magnitude. They claimed that their systems sounded good but after going time-coherent they are now in a totally different league. You can make your speakers time-coherent in one of 2 ways: buy a time-coherent speaker like Green Mountain Audio, Soundlab, Vandersteen, Eminent Technology, some Quad ESLs, some older Martin Logan ESLs to name a few, or, make use something like DEQX to make your existing system time-coherent. DEQX involves a lot more work as you have to do speaker measurements in free space & then apply the correction curves & there's a steep learning curve but the results are worth it, I'm told by reputable people.
Most speakers in the market are anything but time-coherent & inevitably the listener has no/little emotional connection to the music.
What i've found is that, with a time-coherent speaker, even if the electronics is mediocre the enjoyment of music is much more than if the speaker was non-time-coherent.
Time-coherent speakers have benign phase angles in the 20Hz-20KHz region compared to non-time-coherent speakers that have wild phase angles. It's these phase angles that create huge distortion onto the music signal that totally destroys listening pleasure.
See if you can find a time-coherent speaker in your vicinity - a fellow Audiogoner who would be willing to host you, a dealer, an audio show - and listen for yourself. The music rendered thru a time-coherent speaker is leagues ahead. Once you listen to a time-coherent speaker, you'll never go back again I'm pretty sure. FWIW. YMMV.