Sexy visual novels. Usually referred to as "H-games" on OT.
Eroge can cover a wide range of genres. There are side-scrolling shooter eroge, traditional RPG eroge, even bullet-hell eroge. Most of them usually follow a scripted storyline, with a serious of (painfully obvious) branched paths at set intervals.
For example, if the choice given to you is: Who do I want to hang out with?
What the game is really asking is:
Who do I eventually want to have sex with? (Protip: don't pick Frieza)