I'm not overly fond of many remakes, I think the Resident Evil 4 remake loses the original's tightness, and Persona 3 Reload not being the definitive version of Persona 3 should be a crime, though there is one that stands out.

Black Mesa is a fan remake of the original Half-Life, It's incredibly faithful but not to the point of bordering on being a remaster (I'm looking at you, Metal Gear Solid Delta) It genuinely improves on aspects of the original that just weren't as fun. It puts all it's chips in immersion with it's graphics, even being in an engine as old as Source, it looks more like a Source 2 game. Being in Source it also feels a little slower paced, which I personally think fits Half-Life's level design better.

It's also not far from official, Valve allowed Crowbar Collective (the developers) to release it on steam for a much higher price than the original Half-Life.