There are 4 stays so far:
The order, granted in the U.S. District Court for the Western District of Washington, grants a stay of removal for two unnamed plaintiffs.
Judge Leonie Brinkema of the U.S. District Court for the Eastern District of Virginia issued a temporary restraining order requiring the government to permit green card holders detained in Dulles International Airport access to counsel and forbidding the detainees from being removed from the United States for seven days.
The U.S. District Court for the Eastern District of New York has granted an emergency motion to stay the removal of immigrants and refugees detained and prevented from entering the United States as a result of President Trump’s executive order.
The U.S. District Court for the District of Massachusetts granted a temporary restraining order halting the removal of immigrants and refugees. Notably, the order also bars the government from detaining those individuals affected. It also limits secondary screening to the extent permitted prior to the Executive Order and requires Customs and Border Patrol to notify airlines that individuals affected by the Order arriving at Logan Airport will be allowed entry in the United States.
You can read some of them here