I'm a big fan of extreme difficulty in games. If the threat of failure is ever-present then it feels real good when things actually go right. Stalker and Arma are good examples of that.
On the flip side of this, I really can't stand when a game makes itself hard in annoying ways. GTA 4 for example had cool gunplay that was totally undercut by enemies taking half a magazine to kill and then they would just get back up. XCOM EU Impossible difficulty made itself harder by massively buffing enemy aim stats and health, meaning that at times you wouldn't be outplayed by the AI so much as outaimed. The Long War mod makes good on this, by focusing on enemy numbers rather than raw aim and health while giving the player more tools in the early game to deal with them.
A genre (or style, I guess) is really can't get into is that weird classic-mimic thing a lot of platformers and indie games do. There are a lot of things to be learned from old games that can be applied to modern games, but the visual and auditory style isn't one of them. I'll be the one to say it, old games looked and sounded awful. Undertale's music might be top-notch, but those grating menu and textbox noises tear my eardrums apart. I feel like a lot of the reason for those iffy design choices to to look vintage or whatever. Maybe I just didn't experience enough classic games to have this type of thing appeal to me.