James
Brandon has touched on the topic, so I'll just add a bit to that.
One thing is for sure...if you think that 'personal preference' is supreme when it comes to choice in audio...you can multiply that by a factor of 100 when it comes to guitars

What makes a 'great' guitar will certainly depend on the individual. But there are some basics that will be common to just about everybody.
Action/IntonationNo matter is a guitar is $5,000 or $500...if the height of the strings and their setup don't allow the guitar to be played easily (and in tune), then most guitarists will quickly strike it from their 'must have' lists. Similar to audio, most times you get what you pay for and the more expensive guitars play well since there's a lot of TLC put into fret finish, neck finish, nut dressing, etc. This is part of the reason for the elevated prices.
However, sometimes you can find a 'cheap' guitar that just plays better than it should for the $$. These days, these are the Chinese/Korean/Indonesian imported guitars.
These types of guitars (any guitar that is set up well and sounds good) are generally referred to as 'player' guitars in that no matter how 'pretty' they are thay are great workhorses and can be relied upon to get the job done. In the past these are the guitars that you'd see players identify with for many years (Clapton's black Strat/ Billy Gibbon's Les Paul "Pearly Gates"/ Van Halen's striped 'Frankenstein' guitar)
ToneThe 'Other' biggie

This is the sound of the guitar and, of course, the elusive mystery that can't really be explained...but just is (similar to audio, eh

) Most times the tone of an instrument comes down to (i) the wood used for construction and (ii) the pickups.
Certain woods are considered, in general, to be 'better' for tone than others. For example, Korina wood is generally considered to be a warmer wood for tone purposes and is generall well sought after in new and vintage guitars (now there's a hot topic...vintage

). There are varied types of woods that will give you the desired end result, whether one wants a warm tone or a bright, spanky tone. It is common for guitar necks to be made from maple. However, the front part (the fingerboard) will usually be made from maple or rosewood. It is generally considered that rosewood is warmer in tone than maple. So, if you want a 'country' guitar, well, that's an ash-bodied Telecaster with a maple neck. However, the wood alone doesn't tell the entire story. A guitar is 'a sum of parts'

Next there are pickups. This is one of the main area where 'tweakers' will change out parts of their guitars to alter their 'tone'. There's a lot of magic and mojo here....and a little basic science. Some people prefer humbucker pickups for a more compressed, distoted sound. Others prefer the single-coil pickups for a more dymanic response. Big area of 'personal taste rules'

If you want to sound like Mark Knopfler playing Sultans of Swing...well that's a Stratocaster with single coils. If you want to sound like Randy Rhoads and Crazy Train, the humbuckers will serve you better. The other big factor here is amplification.
VintageDifferent than audio, in recent yaers there has been huge movement that 'Vintage guitars sound better than new ones'. In the 1970's there was a period when old guitars were frowned upon and you couldn't give them away. Not so today. Before the 'Market Meltdown' in 2008/2009, a 1959 Sunburst les Paul in good shape would fetch about $250,000

A 1950's Stratocaster would be in the $50,000 range, etc. These are considered by many to be the 'Holy Grails' and are the desire of many. Unfortuneatly, most of these guitars are bought by rich investors who buy them and store them.
So, a simple way to sum up is that many players consider the old stuff (vintage is better). However, if they have to live with new stuff, it needs to play well and sound good. Some people hold a guitars costetics in high esteem. Some say a great guitar is one that has a 'nice top', meaning a nicely stained figured wood top (flame maple, quilted maple, etc).
There are too many factors to list. You could write a doctoral dissertation on it

And then when that's done.....we can move on to something even more 'controversal'...what makes a great amp

...there's a lot of discussion about tubes in that one

Keith