Updated October 2017:
President Trump's Executive Order 13780 Protecting the Nation from Foreign Terrorist Entry to the United States has been considered by the Supreme Court of the USA which has allowed a limited version of the Order to take effect pending a full hearing in the Supreme Court this October - Washington Post 26th June 2017
The ban on people entering the U.S. from six mostly Muslim countries can
apply for now to everyone except people who have a "credible claim of a
bona fide relationship with a person or entity in the United States."
The court indicated in
the ruling that things may change by October. It asked the
parties to address whether the case would be moot by the time it hears it.
Update October 2017:
On October 10, 2017, the U.S. Supreme Court ended one of the lawsuits
challenging the Trump Administration’s travel ban. The Court vacated the
Fourth Circuit Court of Appeal’s judgment in Trump v International Refugee Assistance Project and remanded the case back to the federal appeals court with instructions to dismiss the suit as moot - Constitutional Law Reporter
On September 24, 2017, the President signed a new Proclamation limiting the entry of certain foreign nationals to the United States. This new
proclamation effectively replaces Executive Order 13780, which expired
on that same day. The US Department for Homeland Security published further details - HERE. There is on-going litigation regarding the September Proclamation and this may yet reach the Supreme Court.