A good videogame campaign is fun. When enough things – the gameplay, the world, the story, the writing, the aesthetics, the music – fits you right enough and comes together, it becomes something more than the sum of it parts. I'm also partial to playthroughs of games conceived more so as endless, when they feature natural progression and an endpoint, I set myself a one-off challenge to beat, or I'm just exploring them for the first (or reexploring them for the nth) time. Finally, I sometimes also do special runs/playthroughs of story games, but that's quite rare.
I've had videogames in my life pretty much from the beginning, watching my father play his shooters and flight sims before I could read. Over the years, I have played numerous titles, and realized I have a pretty hard time pinning down what I actually like – it often comes to a certain kind of writing, certain values within it, certain kinds of story and world... and, of course, fun and rewarding gameplay!
...but it might be in my ballpark if it's a campaign FPS, a hack and slash, or an (action) RPG...