Personally, I like it quite a bit and I dunno why. I'll try to self-diagnose.
-First off, when it was released, I had so far been an avid reader of Dark Horse comics set in the "old" SW universe, especially the Tales of the Jedi series, and KOTOR went just ahead and put that kind of feeling into an interactive form of entertainment;
-As a total lover of the Jedi Knight series, which had just gona full derp/retard with the Jedi Academy instalment, KOTOR kinda redeemed the SW videogame panorama a bit, and gave me the chance to see some more lightsaber action on screen (however in its silly, demi-RTWP, boring hybrid form);
-It's Star Wars;
-The story, however banalshitboring one might find it, featured half-decent writing and came across as a decent "fable" kind of tale;
-Bastila, even her low-poly self, is totally fappable to;
-Apart for a few sections/elements, the game was lightheartedly enjoyable and entertaining;
-I did like the D&D-meets-SW feeling, especially since I still was a big NWN fan (online shards, mostly) at the time KOTOR was released, thus the system felt kinda familiar;
-It was the first game (as far as I recall) that allowed the player to play different "classes" from the familiar character stereotypes (smuggler/rogue, trooper, consular/guardian/hybrid) we all knew from the movies;
Well, there's that, so far, and as far as I'm concerned.