Maybe the first Lara Croft with huge triangly polygon boobs? That was kind of awkward because they were trying to go the strong female protagonist route, but also couldn't escape the apparent need for sex appeal.

Another example, maybe not awkward but just poor implementation, would be all the Grand Theft Auto games, where women play no roles other than sex partners (usually paid) or murder victims (often in conjunction with the former type).

Also, I think a huge portion of Japanese role-playing games put forth very awkward presentations of women-as-girls or tweens. One could argue this also applies to the men, who are actually quite feminine in these same games; either way you slice it it seems awkward to me. Whether it's a cultural divide I fail to understand, I'm not sure. I would make exceptions for games that are targeted directly at a younger audience, but in mature rated games it would be more beneficial to have mature looking (and acting) women and men.

One game that I initially thought would have very awkward presentation of women was Heavy Rain, as the first scene in which you control a woman puts you in a break and enter scenario, and eventually implicating her rape and/or death; albeit this was revealed to be a dream sequence (Does that make it more awkward? Or maybe I've put too much thought into one character's own thoughts, fears and motivations.)

Eventually, there were probably only two scenes in the entire game where I controlled Madison and felt awkward (the aforementioned, and the private room in the club scene) but while I personally felt awkward, I think I felt that way moreso for her character; awkward and sympathetic. Then I think for a moment... and I felt that way for all of Heavy Rain's characters at some point, so it was more a case of my own predisposition and axiety toward how much agency is involved. I'm sometimes bothered to think that during that initial scene with Madison that you can do nothing and allow her to be almost completely taken advantage of, while none of the other characters are ever put in a situation like this. Ultimately though, I'm okay with it mainly because you are never trained not to struggle by the game itself (quite the opposite), there is no reward for inaction, and finally because there isn't unnecessary attention drawn to this one scene (a la MW2's "No Russian") by warning the player what is about to take place and allowing them to ... avoid it.

It does play a recurring role in Madison's story and is much a part of her character, so for that despite its potential awkwardness I believe it strengthened her character and the story. Heavy Rain gets a pass where Modern Warfare 2 gets a fail.