This seems to be a hot topic today, so let's de-bunk it thoroughly. Pew Research conducted the most reliable study on this subject which came to the conclusion that MEN are more likely to be harassed over all, and that women are more likely to over-inflate their online harassment (i.e. labelling something minor like 'name-calling' as 'severe harassment). ~However, women ARE more likely to be the victims of severe harassment such as stalking.

Why is this? Truthfully, no matter how you slice it the hard numbers do state that women are more likely to be the victims of this more severe harassment. But the soft numbers start to tell a different story. The Pew Research study states that the most severe form of harassment occurs primarily through social media. In another study on social media, Pew Research concludes that women are significantly more likely to use social media than men (they show an 8% gap). Further, not only are there more women on social media, but Quicksprout shows that they are far more ACTIVE on social media, where the more severe forms of harassment are likely to occur.

Maybe, just maybe, the fact that women are more often the victims of this more severe harassment is not simple because they are women but because they more often frequent the places where it is likely to occur.~ See 'Edit 2'. I was mistaken. Men are actually more likely to be the victims of severe harassment than women according to the Pew Research study.

Links:

http://www.pewinternet.org/2014/10/22/introduction-17/

(A 'quick facts' version of the above study: http://www.pewresearch.org/fact-tank/2014/10/30/5-facts-about-online-harassment/)

http://www.pewresearch.org/fact-tank/2013/09/12/its-a-womans-social-media-world/

http://www.quicksprout.com/2014/10/01/who-is-more-active-on-social-media-men-or-women/

Edit: There is also another somewhat-informal study that showed high-profile men where substantially more likely to experience all forms of online harassment than high-status women but I can't seem to find my bookmark. If anyone has a link to it, please let me know and I'll add that in here as well.

Edit 2: /u/xNOM pointed out my misinterpretation when I re-read the Pew Research study on harassment numbers. It turns out that only women 18-24 are significantly more likely to be the victims of severe harassment than men 18-24. When looking at all ages, men are more likely to be the victims of minor AND severe harassment overall, with women being subject to stalking and sexual harassed in particular.