-Generally speaking, the most common victims of assault and robbery among travelers are lone men. This is because we tend to assume that our sex makes us safe, meaning we'll take risks that women tend to avoid. The most common mistakes are being any combination of lost, alone, and/or drunk at night. In most places, this is dumb. In places where you don't know the language, don't have anyone you can call up for help, and don't know all the ins and outs of things like local law enforcement, it's even dumber. Testosterone doesn't make us invincible (it just tries to tell us we are), so while you may think you are less likely to be attacked than a woman, don't let that lead you into stupid situations.
-As a man, in many cultures, you will be often be expected to drink a lot more than you might at home. Do your homework, and, know whether it is offensive for you to refuse a drink. Women are allowed to do this almost universally. For men it's sometimes harder. If you're up to the challenge, make sure you are either already where you'll spend the night, or have someone who will be sober to get you home (and make sure they actually know how to get you home at the hour you want to go). This is much more important while traveling than it would be when you're in a country where you speak the language, know the area, and have friends who will come looking for you and help you out if something goes wrong.
If you're not interested, take small sips, keep an eye open for a place to drain your drink unnoticed until it's half full, then pretend to take sips from that. A full glass points out that you're not drinking. An empty one signals to your new friends that you want another drink. If you have choice of drinks, mix yourself something that looks like it's alcoholic (but isn't) and get possessive if anyone else wants a sip (or pretend you're getting a cold and don't want to make anyone else sick).
If you do not drink for personal or religious reasons, this is usually accepted, though with a similar air as telling people in a steakhouse that you're vegan. More often if you declare that you are recovering alcoholic and want to drop it, then your choice will be almost universally respected (though keep in mind this can lead to odd situations later).
-In many countries, you'll get a lot of physical contact from other men in ways you might not be used to or comfortable with. One male traveler I met who spent a lot of time with Korean exchange students reported heterosexual Korean men would often caress and pat his butt with their hand while talking to him, and be completely mystified as to why he found this startling or confusing. I never experienced anything quite that intimate, but when you're in a new country you'll sometimes be expected to do things like hugging, holding hands with or kissing other guys on the cheek. Not doing this usually gets the same reaction as refusing to shake someone's hand at home, so either go with it, or make sure you can explain yourself adequately so that people won't be offended.
-If you need to shave daily and don't use an electric razor, bring extra blades/cartridges. In places where the local guys aren't able to grow facial hair as easily, you might have a hard time finding the kind you want. In big cities, Gillette and Schick are easy to find, and I'm pretty sure Antarctica is the only continent I haven't seen somebody selling a Mach 3 cartridge somewhere. If you do use an electric razor, double check what kind of power outlets it can handle, especially if it's built for 110v, 220v, both, or something else.
-Rule of thumb for the heterosexual traveling man: if she seems like she's too good to be true, she probably is. While it's true that being foreign can make you more attractive, there are plenty of scams involving a skilled local thief being let in by a smitten male traveler, enjoying a night of passion, and then helping themselves to the passport, credit cards, and other goodies in the room while the guy's asleep. This doesn't mean that you should avoid all lone women while traveling, it just means that that slightly shy girl in the group of friends someone introduced you to is probably safer than the girl who came alone across half the bar to say hello in your language and massage your thigh. Also be aware that sometimes, in select countries (most famously Thailand), "she" might not actually be a, well, she.
Less risky but more common are simple scams targeting men where an attractive young woman is in some sort of distress and seems to think only you can help her. This can either simply be a way to part a heroic fool and his money, or serve as a distraction while an associate helps him or herself to your pockets and bags. Have a heart, be compassionate and helpful when you encounter someone like this in need, but try to help in other ways than simply handing over cash, and watch your stuff. If the damsel in distress get increasingly angry and frustrated by your offers of non-monetary help, chances are it's a scam.
Yet another variant is girl or group of girls that ask a lone foreign man to come with them to a bar, cafe, restaurant, or tea house, and everything rosy until the guy ends up being handed a bill for ten times the going rate of whatever is ordered. This is especially common in major cities in China. When invited by to this sort of thing, be friendly, and suggest a place of your own. If they get pushy, smile, tell them it was nice meeting them, and move on.
-Bring condoms from home. In a perfect world, this would be the responsibility of both genders, but in reality, it's usually the guy that's expected to supply these. Local brands are more likely to break than the ones you'll get back in the west. Also, in places like Asia, I've heard reports that the size can be a little uncomfortable for westerners, but this could be a myth. Better safe than sorry in any case.
-In the tips for women, Sonia, Sonja and Emily all emphasized covering up when the local women cover up. In a small number of cases, namely Muslim countries, this applies to men too. The consequences are a lot less annoying, but if you're wearing shorts or short sleeves where you shouldn't, you'll simply be refused entry or service in certain places. Much more common are places where you'll make people a little upset by wandering around shirtless. Also, even in area where it's fine, if you have more chest or other body hair than the local guys, expect a little unwanted attention (some people without chest hair don't seem to understand that pulling it hurts, and that doing it to a complete stranger is weird). As we said for the women, watch the locals and follow suit.
That's a start, I think. Once again, I encourage any men out there with travel experience to share other tips they have for us guys.