Participating in this past weekend's Ludum Dare, Robert Yang created Condom Corps based off the theme "It's dangerous to go alone! Take this!" For this game, this is a condom that you shoot at people to ensure they're having safer sex. The trick to it all is that you have to stare at these silhouettes and determine their package size, then shoot the appropriately sized condom into their hand (which the introductory instructions refer to as a payload).
What immediately came to my mind was a game from this year's Global Game Jam I also talked about here: H.I.V. Extinction 1981. The view you have is one to which many gamers will be familiar if they've ever used a sniper rifle in a shooter, so the theme of guns and sex is again explored. This time it focuses less on that gun being your penis, and puts the focus on objectifying and quantifying other mens' penis size.
The entire premise borders on the absurd, from the subtitle: "It's dangerous to go alone... take this condom, bro," to the fact that it's also a game where you gain more points for matching colors, so you look for people of the same size to shoot. It seems as much a tongue-in-cheek acknowledgment of hotel sex parties that can occur, as well as a pre-occupation with penis size, though the emphasis is not on the 'bigger is better' mindset.
Further adding to the sense of absurdity is when you manage to incorrectly judge a guy's package. A too-small fit and the condom is too tight and strangles him. Too large and it slips off and he contracts herpes. And dies. Considering that herpes can be transmitted through just skin contact, thus not wholly prevented by using a condom, there's a certain measure of melodramatic hyperbole in effect.
As a whole package safer sex message? I can't speak to people working in that field professionally, but when I was volunteering at such places in Chicago, the emphasis was on risk mitigation, and condoms were the best resource for safer sex practices outside of giving people knowledge/information. Considering many people will ignore the latter, condoms became the number one resource by default. The importance in this game seems to be a parodic take on making sure people realize they need to actually get condoms that fit them, rather than playing an ego game. Of course, even when you get it right, the message is a somewhat lackluster, "The sex was alright I guess!"
As far as smaller, browser-based games go, the field of exploring safer sex through them is a theme I would like to see explored further.