House Party (which is available for free right now on the site below) is similar to many browser games in which your choices affect your progress as you progress through the game, but the game is played as a first-person game. An RPG with interactive playable models, characters and physics like the aforementioned Leisure Suit Larry.
However, I tend to take these games in a much more obscene direction than the LSL series. The games will have a lot of profanity, nudity and sex, but hopefully they will be just as fun and engaging.
However, right now I don't have much of a storyline, just a few tasks to complete while I'm working on the game mechanics. However, there are multiple story paths and different outcomes based on them.