Below is a description I gathered, and granted its from Wikipedia, I'm sure someone can verify this:
Whereas the Shiites believed that the imamate (leadership) was the sole right of the house of Ali, the Kharijites insisted that any pious and able Muslim could be a leader of the Muslim community. And whereas the Sunnis believed that the imam's impiousness did not, by itself, justify sedition, the Kharijites insisted on the right to revolt against any ruler who deviated from the example of the Prophet Muhammad and the first two caliphs, Abu Bakr and Umar. From this essentially political position, the Kharijites developed a variety of theological and legal doctrines that further set them apart from both Sunni and Shiite Muslims.
Kharijites were also known historically as the Shurat (Ar: الشُراة), literally meaning "the buyers" and understood within the context of Islamic scripture and philosophy to mean "those who have traded the mortal life (aldunya) for the other life [with god] (alakhera), which, unlike the term "Kharijite", was one that many Kharijites used to describe themselves. The only surviving group, the Ibāḍī of Oman, Zanzibar and North Africa, reject the "Kharijite" appellation and refer to themselves as ahl al-'adl wal istiqama (أهل العدل و الاستقامة) ("people of justice and uprightness").
I'd consider myself politically and socially a leftist/socialist/borderline-communist and so these guys naturally appeal to me. And their description does accurately match a lot of the so-called "Salafi" groups like Al Qaeda (if they even exist) or the Muslim Brotherhood of Egypt or Hamas or Al-Shabaab or the Taliban and virtually every other currently-active Sunni-Salafi political and armed movement - would you not agree?
I'm confused by this a little bit, virtually all current pious/fundamentalist Sunni Muslims who describe themselves as anywhere near political fall in the same thought process as the Kharijites. They all want to overthrow current Muslim rulers (Saudi royal family, Hosni Mubarak, Mahmoud Abbas, Sharif Ahmed...the list goes on forever) in favor of more pious leaders chosen by the public.
Someone clarify this for me because it seems like today, Salafism & Islamic Military and overall Revivalism is virtually a nickname for Kharijism.
Not to say I don't support free enterprise but I also am very supportive of socialism and leftist politics. 