The only game that ever gave me real pause due to it's weirdness was Deus Ex Machina (48K). Everything about it was "weird" right down to having to sync the soundtrack audio tape with a countdown screen prompt. The narration, actual music, the slighty hypnotic and psychadelic stuff on screen and having no idea of what was going on was both fascinating and slightly intimidating at the same time.
It's not a good game by any measure, mostly a sucession of mini games that you can (kinda) play. I don't think i've ever reached the final credits back then but the experience on the whole, its "weirdness", stuck.
I remeber coming across weird games later or, like Vigil: Blood Biterness which was all around weird but plagued with tech issues, and some others but none of them really had the same impact.
Nowadays i don't go out of my way to deliberately look for novelty or "weird", i kinda "stick to the point". As the years pile on it's harder for the weird to have a meaningful effect anyway so maybe i've become a bit lazy in that regard. Also pressured, time wise, by the games on my library i haven't played, the games i want to replay and all the games i already know i'll eventually buy with no real expectation of ever playing them - all of it combined keeps me focused on what's already under my nose in a slightly unhealthy manner, in a check list like mentality of sorts i guess.
That isn't to say that there's no weirdness or suprises in my relationship with games. For instance, my favourite genre for the longest time were FPP P&C's and i never paid much attention to action games. Today i wouldn't be able to say which was my last P&C or how long ago i played it while i find myself slightly addicted to souls and souls-like games. In my mind the natural order of things would/should have dictated a reverse order but, it is what it is, weird.