I am Greek holding a Greek passport and travelling to Cancun directly from Amsterdam. Do I still need to apply for ESTA?
The only ESTA I know of is a system to obtain authorization to travel to the United States of America. Your description of your itinerary doesn't mention traveling to the USA at all, so you do not need to apply for ESTA.
If your flight involved a connection in the USA, then you would need to apply for ESTA. But since you say you are traveling "directly" from Amsterdam, I presume that is not the case.
ESTA is a Unites States government requirement for foreign citizens.
However, if you're not visiting the USA, you have no need to get it.
So as long as your flight from Amsterdam to Cancun (or any others) don't transit, land or layover in any US airport, you do NOT need to get this, no matter what your citizenship.