Some games are gender neutral, and I appreciate it. It doesn't matter what your character's gender is in Settlers of Catan, because everyone has the same little houses and cities and fences. In both Forbidden Desert and Forbidden Island, the characters are little genderless pawns and the descriptions of the various roles are given in terms that don't use pronouns. These games feel particularly friendly, as I can choose any role that I want and play it as a female character if I want. The pilot and the archaeologist might very well be me.
The second type of games, games that handle female characters really well, is depressingly slim. In fact, the only game that I can think of is Pandemic (together with both expansions, On the Brink, and In the Lab). In Pandemic, there is a wide variety of character roles, split approximately equally between male and female characters. The female characters are at least as powerful as the male characters, the language on the descriptions is neutral, and, most refreshingly, the characters seem to be dressed like people who would actually work in a lab. The lack of objectification or sexualization of the women in the artwork means that I can recommend the game to my friends or suggest that we play it without having to qualify it or feel uncomfortable about some of the characters.
There are a few games that handle female characters pretty well, although I still have a few criticisms. Arkham Horror is my favorite board game. I love playing it, and I will take every opportunity to introduce people to it. Overall, it handles female characters well. About half of the characters in the base game are women (7/16), and about half of the characters are female once you add together all the expansions. None of the character skills, abilities, or items are dependent on gender. The female characters have a wide range of abilities and power levels, and some of the most powerful characters are female (including Carolyn in the base game and Patrice from one of the expansions). But the artwork is occasionally unnecessarily sexualizing. Take two characters in the base game, Jenny and Mandy:
True, Jenny Barnes is the dilettante, but her pose is ridiculous and it would have made more sense with the general feel of the game if she was wearing a stereotypical flapper dress (perhaps also with that 1920's flatter figure). Or take Mandy Thompson, the researcher. Note that while her face is in shadow, the light highlights her cleavage. This type of artwork that sexualizes certain characters makes me uncomfortable.
Zombicide is another great game that has issues with female characters. It does some things well. Items are not gender dependent (anyone can have a pistol or Molotov cocktail), characters gain xp in identical ways, and it turns out that the women are some of the most powerful characters. But then there's the artwork. Take a look at the art for the two female characters in the base game, Amy (the Goth) and Wanda (the Waitress):
I'm a little conflicted about the artwork, actually. On the one hand, it fits with the style and overall feel of the game, but on the other hand, it appears that if you are a woman fighting zombies you are constrained to a short skirt and either tight, revealing clothing or lot's of midriff. This is very different from the male characters, for instance, Josh, who manages to fight zombies while wearing a loose sweatshirt and ripped jeans.
It really gets worse in the expansion that we have, though. Toxic City Mall is a pretty good expansion, until you look at the artwork for the two female characters, Neema (the Executive) and Elsa (the Cat-Burgler).
Neema and Elsa are blatantly sexualized. There is no reason for Neema to be wearing a skirt slit up to her thigh, a shirt that is much too small, or stilettos. I suppose I can understand why a cat burgler would wear latex (not because it is practical, but it is stereotypical) but that doesn't explain why the suit is unzipped to the waist or why she is wearing stilettos, and the pose is just weird. Contrast these to the two male characters available in the expansion (Raoul and Derek) who are both depicted wearing loose, practical clothing and standing in powerful stances. The depictions of Neema and Elsa make me uncomfortable playing the game. More than that, though, I feel uncomfortable recommending the game to friends, particularly women. I find myself apologizing for the artwork, which makes them uncomfortable.
And, finally, there are some games that are problematic in how they treat female characters. I like Shadows Over Camelot, but it really has problems with how it depicts women. Despite the box artwork, which shows women on both sides of the battle, there are no playable female characters. This is depressing, and a major reason why I was reluctant to play the game at first. I want to play a knight who is also a woman. There's no reason why they couldn't have included a female knight or two, either, as the game isn't historically* or mythologically tied to one particular version of the King Arthur legend, so far as I can tell. But it gets worse. Not only are there no playable female characters, but the cards that you draw (essentially event cards) are overwhelmingly negative in their depiction of women. In the black cards (basically negative events), there are three different women you can draw. The Morgan cards are all horribly nasty. The Vivien card is also pretty horrible. The Guinevere card varies, but is generally really bad. (There is only one black card that has a named male character on it, the Mordred card.) And in opposition to this there is only one white card, or positive element, that is a woman, the Lady of the Lake card. The cards are overwhelmingly negative in their depiction of women. Overall, this leads to a game that feels overwhelmingly negative in its depiction of women.
Munchkin, though, is the game that I personally find the most offensive (to the point where, having played it once, I said that I would never play it again). I understand that it's supposed to be playing on tropes, and is supposed to be funny, but I just find it offensive. It contains such cards as the chainmail bikini and revealing costume. It's been a while since I played it and I don't have the game in front of me (thank goodness) but as I recall, it also involved artwork where women are defined by their busts, equipment that could only be equipped by characters of a certain gender, and so on.
Overall, the poor handling of female characters by these board games makes me feel uncomfortable. I'm hesitant to recommend games like Zombicide and Shadows Over Camelot to my friends because of these problems, despite rather excellent gameplay in both instances. It also makes me suspect that many of the game creators were not considering women as players when they created the games.
I'm only speaking for my own experience, but I expect that I'm not the only one to be troubled by the depiction of women in a lot of these board games. It's disheartening, especially because in a lot of these cases the problem could be easily solved with minimal effort. And, to speak more broadly, it is one of the reasons that some women feel uncomfortable getting into gaming.