How many criteria for one game so it becomes interesting for me to play, or general criteria in games that grab my interest? Because so far I see people naming quite a lot, and im thinking its to the point that a single game that fulfills them all sounds close to a wonder.
In any case, both times im looking for things that have variety. I like to see different things, not necessarily all in a game as that could lead to a clusterfuck of things thrown in without all thought through. Im talking about characters that have some personality, but not for the sake of it. Dont need to have polarizing characters that are like day and night, just something different between them, be it in hobby, likes/dislikes, up to visuals. For example while big breasts are more than great for me, if every character has them its obviously not really special anymore.
The same thing applies to scenes or fetishes, maybe thats on me since I can get behind most of them, but I also want to see more of them applied. And while I like the family setup and the incest fetish is a nice way to spice things up, I really want other things from time to time, or at least mix it up with something else.
And you are asking for criteria in an Adult Game, and for me most of the programs there are right now are more like an interactive porn book with pictures that im clicking through instead of having something that qualifies them as a game. Theres no real game to it, and no, picking different options for a different character route isnt really cutting it. Theres books like that already, jump to page 53 for different outcome. Im still playing most of them, just have to have something else between them to not see the same all the time.
To name a few examples, give me something like Lab Rats, where you have to balance the use of the anti-inhibition serum you give them, and they at least have sexual preferences, and different body styles.
Or something like Misadventures of Agent Romanov, where an alien parasite/tentacle/whatever it is (Venom from Spiderman fits pretty well) affects the character and the parasite, while not completly overtaking the MC, makes her do things a bit out of her comfort zone, which can also be influenced by character stats you chose. Also probably tentacle sex, and a hot redhead, sign me up.
Last very different example is Inheritance, a mostly text based game with art added as "support" in which you inherit a mansion with surrounding land that also comes with two slave maids (theres more to it of course, they got treated quite "bad" from the last owner, your estranged uncle). You can already see the scope of it and chose things to your liking, but it comes down to, what do you want to do with them, nurture them and give them hope, or torture them (mind and body wise), play them out against each other (they are sisters by the way), or give them hope and then lead them to their downfall again.
Yes, sounds evil, can be evil, but it will only be as evil as you want it, and shows what real choice making in a game can be. And definitely evokes a lot of wanting to protect them, while also wonderning what would lie on the other paths.