edit: We need definitions for these terms solid enough to put in the sidebar, this post is an attempt at working towards that. We can't just keep all going around saying "Alpha" and "Beta" and having everyone mean something different.

edit 2: Here's another link to socio-sexual categories that seems more thought out.
On this list I'd fit Sigma best.

Alpha Male: You are confident and your own man. You do your own thing and have complete confidence in everything you do. You have your self doubts, but you don't let it cloud your judgment and logic. You are well liked by almost everyone, and you just have an easy charm and swagger about your presence. Women are drawn to your charisma and presence. You enjoy being social and having lots of people around, you need constant social interaction otherwise you start to feel depressed or "drained" like your batteries need to recharge. You are a natural leader who actively seeks out leadership positions. Conversely you do not do well answering to authority.

Beta Male: You are kind of shy and introverted and not very confident in yourself. You are constantly plagued by insecurities and self-doubts and you can never commit to anything in the fear that you will fail in it. You are somewhat liked by people but they tend to look at you rather condescendingly and woman tend to friendzone you. You are nervous around other people and social situations because you're always afraid that people are judging you. You are a born follower. As such these types often do well in specialist positions like research science, especially in the fields of physics and chemistry. Customer service is your nightmare.

Omega Male: You are very much like the alpha male, the primary distinction being that where the Alpha "recharges" in groups you "recharge" by being alone. Like the alpha male you are confident, intelligent and have a sense of charisma about you, but unlike the alpha male, you are completely your own person. Your strength doesn't flow from those around you, it comes from within. You do not need anyone, and you can even be emotionally distant due to your complete self-possession, though you won't see yourself as distant at all. You trust few people and foster even fewer intimate relationships, people must earn your trust, it is not given freely. Omegas generally make the best leaders, though they never seek out the position. More accurately, it is cast upon them by their peers at which point they reluctantly accept the position until their primary goals are achieved; at which point they seek to leave the position as quickly as possible, which is the polar opposite of the Alpha Male. George Washington is famously Omega in leadership personality and was called "The greatest character of our age" for stepping down from his position of power willingly, despite popular demand for him to stay in power.

Gamma Male: You are sort of the "invisible" guy. There is nothing really spectacular about you. You are not a beta, but neither are you an Alpha or Omega. Your personality and presence usually blends in with the rest of the room and you're just sort of...there. People like you just fine and you usually don't have too much trouble with girls, but all the same, there is nothing particularly memorable or remarkable about you. You are not a born leader nor an inherent follower, although you can take on those tasks depending on the situation. In social situations you can often be a neutralizing force, diffusing situations that would otherwise become dramatic. Bureaucrats and diplomacy are two strong fields for this type, though technical tasks performed in isolation, not in a team, are another avenue.

Sigma Male: You are a manipulative mastermind. You are a spider waiting to lay your trap. You possess a cunning, intuitive mind and can sway people to your will. You don't have the casual swagger of the alpha or the omega but you do have a clever presence about you and people tend to be both wary and respect you for that. You can often be even more powerful than the alpha or the omega male in social situations due to your ability to persuade and manipulate them, though never on points they care about. You are neither a follower nor a leader but rather a wild card. Cyrus Tolliver (Deadwood) is probably the best example of this type.

So guys, having all this information about different societal types at your disposal, where would you say you fall?

Personally I'm pretty firmly in the Omega camp, though I certainly display attributes from Alpha and Sigma at times.