Always loved videogames enemies with names and personalities, at a time where most of them were indistinct canon fodder. Games like Carmageddon let you build rage and rivalry with specific opponents. "Oh that guy, again, okay you'll see this time". Even games like Technocop had you go after bosses that were presented by a "wanted" poster. I never played Hoverforce (aka Resolution 101) but I wanted to just because it had a screen in your cockpit dedicated to the face and reactions of your opponent. It makes them more real, more like imaginary interlocutors.
I suppose the Pac Man ghosts would qualify, but I wasn't really a Pac Man person. A primitive form of it would be the sprite that appear from the same place on the same screen of a shooter/brawler, even if it looks like all the others. You can build some specific resentment or familiarity with it, but it's fleeting (you can feel the same for your pencils). The Civilization games do it well, with your opponents, you can get passed at them, get back at them, or be forgiving to them. Some open world games that generate names for NPCs can give you that feeling at time, even if these NPCs are usually short-lived. And of course, the nemesis system (the Shadows of War one, not the scripted RE character) is brilliantly built up around these sensations.
But I still consider Carmageddon the best example.