Seeing your analogy to books and movies, I'm going to assume that with "games" you mean the more story-focused onces with little to no branching. That way I don't have to point out what you already know ("make different choices in these games", "play to beat your score", "go for speedruns", and so on). In fact, I'm going to talk more about books and movies that I've seen more than once, because those same principles apply to games (with heavy story-focus) as well...
What is it really that draws you into a story (be it in a movie, book or video game) ? Discovery is certainly among the reasons, and that obviously diminishes once you've seen all the medium it's presented in has to offer. It is, however, not the only reason.
I've reread my favorite books three or four times. Why? Not because I didn't know what was going to happen, but exactly because I did know. I liked the characters, liked the atmosphere, the pace, how things were presented...it's like revisiting friends (I hope you don't get tired of
them ).
Movies are the same, but perhaps with some twists. Parts of movies can be entertaining or exciting even though you've seen it before. If the movie has a plot twist in it (you missed the first time), see if you can see it coming now.
And if a film is truly, TRULY great, then it not only has you engaged in an entertaining way but has given you something to think about. Which you can use when you look at it again. Fight club, for example, has all sorts of anarchistic/anti-social messages that are pretty deep if you really think about it. It provides means where you wouldn't really expect it the first time around.
And games? I can't speak on behalf of all games, and TBH I don't even
want to talk about most RPG's*. But here are a few I replayed, even though I've got plenty of games in my backlog:
* New Super Mario Brothers Wii: okay, this one's not really fair: I replayed it with my (former) girlfriend. Co-op is a totally new experience. And she went from "how do I jump ON a koopa?" to "okay...I can hold my own".
* antichamber: as mentioned earlier: leave some time between the playthroughs. I love this game so much that I almost wish I can just erase my built knowledge of it, just to be able to experience them again. But luckily for me, I had forgotten quite a bit, and happily went through it relearning those (it helps that the ones I did remember were never a chore)
* limbo: this one is purely for the mood. It's amazing how much the game tells without actually using words. Oh, and also...the second time I was puzzled by the fact that the game had, in fact, puzzles (I had forgotten just about all of these).
* Braid: this game is actually much better the second time: the story makes more sense and the puzzles are less hardbitingly frustrating (though still pretty hard, unless you've got an extremely good memory).
*just a personal preference...quite some RPG's treat the story as a means to string a bunch of fancy-schmancy cutscenes together