Series such as Sakura Wars combine tactical RPG gameplay with dating sim gameplay.
The first game that set the standard for the dating sim genre was Dōkyūsei (1992), which relied more on timed events than dialogue choices.
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If you dig deep in the archives you might also find some obscure 15 year old Japanese sex games..
But if you stick to the latest games you'll have a good chance of playing something that will keep you literally up for hours!
These games also often involve raising stats that reflect the player's skills.
The term later expanded to encompass any game with romantic simulation elements, even when combined with other genres.
Katawa Shoujo is surprisingly well written and well put together.
One of the only choose your own adventure style games I have actually gone through multiple times.
Make sure to leave the adult scenes on, at worst they're funny filler, at their best I can't imagine the story without them. Persona 4 is basically two games, a dating sim in the real world, and a fantastic jrpg in the tv world.
The way the mesh the genres just enough while still retaining their separate flavor is impressive. You can also look around in the OELVN community, on the Ren'py site I think, for some free dating sims.
Memes, comics, funny screenshots, arts-and-crafts, etc.