There are many, many, many, different sub-groups to both the "left" and the "right".
First, let's start with where the use of the term "left" in polity vocabulary comes from.
http://en.wikipedia.org/wiki/Left-wing_politics
"In
politics,
left-wing,
political left,
leftist and
the Left are terms used to describe support for changing traditional
social orders and creating a more
egalitarian distribution of
wealth and
privilege. The phrase
left-wing was coined during the
French Revolution, referring to the seating arrangement in parliament; those who sat on the left supported the
republic, the popular political movements and
secularization."
It is generally understood among progressives and radicals that the left represented a break from tradition - a defiant stand against the existing social order which at the time was rife with hierarchy, privilege, exploitation, and fairly unpleasant state oppression of the poor.
Since then, the term has come to mean pretty much anyone who challenges the existing social order in an effort to attain what they believe to be "social justice" by minimizing or eliminating social inequalities which are the lack of rights (such as property, legal, voting, freedom of speech and assembly), access to education, health care, etc for any kind of group but mostly including ethnic minorities, women, queer and transgendered people, and so on and so forth.
Now, the waters are a little more murky. Nationalists like pro-fascist nazis are generally regarded as being on the right because they are seen as standing up for a social order that has oppressed ethnic minorities since it was profitable to do so. This however does not mean that all nationalist movements have been racist. I just can't find a single white nationalist movement that wasn't. The Mexican revolution was nationalist but it was heavily influenced by lefty authors and organizers from anarchism like Zapata who was elected to lead a peasant army.
But that is the far right - the tinfoil right. Next to them are people like Alex Jones and Ron Paul who are slightly less racist and weird. Somewhere in between them and the Nazis are anti-immigrant white supremacists like those dudes in Az. that carry guns around the border.
Slightly just next to them are Republicans. There are two types of Republicans. Politicians and voters. Politicians lie to the voters so that the voters will tolerate the growing corpocracy, imperialism, Capitalism, GMO frankenfood, totalitarian anti-citizen spy programs, torture, destruction of our natural resources, drug criminalization, rising unemployment due to globalization, private prison industry and more fun stuff.
Slightly just next to them are Democrats. There are two types of Democrats. Politicians and voters. Politicians lie to the voters so that the voters will tolerate the growing corpocracy, imperialism, Capitalism, GMO frankenfood, totalitarian anti-citizen spy programs, torture, destruction of our natural resources, drug criminalization, rising unemployment due to globalization, private prison industry and more fun stuff.
See what I did there?
Libertarian Party members are usually about reduced government, personal freedom, and free market capitalism. I get along with them most of the time except for the free market capitalism and permitted existence of a federal government. BTW - Capitalism is not the only market economy and everything you love about market economies is perverted and contorted under Capitalism to maintain the anti-freedom corpocracy. Fuck monopolies.
Also I want to make it abundantly clear that every president who ever lived and presided over the USA has been a genocidal misogynist and generally a very bad person. From Washington to Obama, every one of them has been complicit in genocide (which is unjustifiable and perhaps the most egregious human rights abuse) and class war against the poor. All of them further sold us out to wealthy companies and businessmen.
Somehow we were convinced that democracy, the highest form of government and polity, a beacon of egalitarian decision making, meant electing people to make decisions for us. It even happened in Russia to people who believed in the promising message of the new socialism ala Marx and Lenin. Somehow the people affected by decisions lost the ability to make them and a ruling class emerged in Russia, whereas one had already been established in America. To this day we still believe foolish prattle that this is a free country - all the while decisions about what we eat, watch, read, listen to, who we love and how, the work we do and the pay we get (or don't get), and so much more are being made for us. The claim is that we are able to elect people who represent us, however an overwhelming majority of wealthy people in the state and federal governments clearly indicates we are not represented considering how many people are below or at the poverty level in this country.
So what is the alternative? Only direct democracy. But what kind and who has the right one? There are some good ideas out there I feel. I am a social anarchist and I favor anarcho-communism, which is not so much a system itself but a philosophy which has guided the creation of egalitarian radically democratic systems like anarcho-syndicalism, participatory economics, and more. I distrust market economies because they all remind me too much of Capitalism but I wouldn't mind participating in anarcho-mutualist economies if one near me had goods I needed or services required that I could provide. Anarcho-mutualism seems like the most libertarian and yet socialist economic system that any fan of markets could come to embrace.
So I guess I'm lefty. But I should point out that there is a term worth searching called "Post-Left Anarchism". I don't know how I feel about it to be honest. I like some things some post-leftists have said, such as Bob Black. But not everything I agree with. Such is life and the diversity of minds, right?
I believe that communism, like love and respect, is not something that can be imposed from the top down. I believe it is something that must be constructed from the bottom up and that any amount of coercion, domination, or exploitation is a sad perversion of communist ideals. I believe we should be free to determine who with, what and how much to share. I also believe that commodities have innate attributes which lend them to certain economies more than others. For instance I believe that the gift economy model of Open Source Software makes a lot of sense because of the ease with which such information is added to and distributed. While at the same time I feel consumables may be appropriately traded on a mutualist market place or distributed via syndicalism or participatory economics. I reject intellectual property rights, favor use based land economies, totally support worker self management, community-based direct democracy, pervasive and ubiquitous community and personal sustainable organic gardening, and complete personal freedom which does not mean the freedom to oppress, dominate, coerce, or exploit anyone. So for instance, society should tolerate marijuana use but not rape. Using marijuana doesn't coerce anyone into doing something they don't want to, nor does it exploit them.
Anyone looking to find out more about anarchism can look at the FAQ which does a good job of criticizing both left and right-wing political ideas while presenting a clear and concise definition, survey, and case for anarchism. It also has an interesting article about how justice would be approached in an anti-authoritarian society; section I5 I think.
http://www.infoshop.org/faq/index.html
If you'd like more info than that, like about what forms of decision making, organization, and economics anarchists support you can PM me for links.