The Syrian Electronic Army is a unique group. They sprung up in 2011, and backed the regime of Syrian President Bashar al-Assad (it's thought they could be supported by the Syrian government). While the group isn't very sophisticated, they've attacked a large number of high-profile organizations and hundreds of websites. They primarily use spamming, malware, phishing, and denial of service attacks. Their first two years of existence saw just a handful of attacks, but in 2013 and 2014 the group launched dozens each year.
Highlights include their hacking of President Barack Obama's Twitter account:
And the AP:
Of course, they even have their own Twitter account.