¡Ya basta! is a phrase in Spanish roughly approximate to "Enough is enough!" or "Enough already!" in English. It has been adopted by several Latin American insurgent groups as an expression of affront towards issues that sparked the original dissent. Its adoption by the EZLN in Mexico as the movement's motto is exemplary of its popularity and ability to rally diverse ideologies under a common goal. Grammatically, there's little difference between ¡Basta ya! and ¡Ya basta!, and both are correct.
According to Thomas Oleson, there is also a website, separate and distinct from the Italian solidarity group, Ya Basta! The Ya Basta website started in March 1994 by Justin Paulson, being one of the first websites to carry EZLN material.
"Ya Basta Association" was the name of a major anti-capitalist activist network of groups in Italy which played a central role in the Anti-G8 protest in 2001. They are known for their adoption of sophisticated direct action tactics and for making suits of armor out of street garbage and recycled materials. Ya Basta Association is sometimes associated with the 'White Overalls' who appear in many protests heavily padded.
Another movement with a similar name is Spanish ¡Basta Ya!, an organization opposing the violent Basque separatist organization ETA, which carries out attacks in the Basque Country to demand its independence from Spain and France.