I agree completely with PaulH. UaKM is the game that got me into the series, and in its day, it looked phenomenal. I'll admit, graphically, the game hasn't aged well, and the controls predate the industry having a solid grasp on how to handle 3D environments well (but, once you get used to them, are entirely usable), but the writing keeps it among my favorites.
Now, that said, UaKM was Access pushing into unknown territory; they were frequent technology pioneers in the game sphere. This was them figuring out how to make this sort of game work. And they took those lessons, and made Pandora Directive. The world was larger and more detailed, the characters were deeper, and the FMVs were much better composed and directed (and the story, eerily prescient at times). Similarly, the direction in Overseer remains quite good, though they were kinda forced to make that one in a hurry.
I still go back and play UaKM and TPD every couple years or so. It's been a while since I last tried Overseer, though -- mostly due to issues getting it working on modern computers. But, for me, it's less about the game itself (though I do enjoy the puzzles still), and more like going back and rewatching a favorite movie, or rereading a beloved book. It's the stories I enjoy. They have a brilliant mix of humor and tension, full of endearing characters (and, in the case of TPD, a villain that you just love to hate) and a really fleshed-out world.
But screw the fireball room. Seriously.
That alone is the only reason I'd want to see the games remade (as opposed to just rereleased). The mouse movement is serviceable for exploring static environments, but is maddening for navigating a narrow and winding walkway through a dangerous environment.