Here is the status of flights by key airlines and civil aviation authorities:

American Airlines
Flights to China, Hong Kong, Milan suspended.

Air France
Mainland China flights suspended.

Bahrain Civil Aviation Affairs
Suspended all flights to and from Iran, Iraq, Lebanon and the UAE.

British Airways
Mainland China, Italy, Singapore, and South Korea flights suspended.

Delta Airways
Mainland China flights suspended.

easyJet
Italy flights canceled.

EgyptAir
Mainland China flights suspended. 

Emirates
Mainland China, except for Beijing, and Iran flights suspended.

Etihad
Mainland China, except for Beijing, and Iran flights suspended.

Iraq
Non-Iraqi travelers from China, Iran, Thailand, South Korea, Japan, Italy, Singapore, Kuwait and Bahrain banned.

KLM
Mainland China flights suspended.

Kuwait Civil Aviation Authority
Iraq, South Korea, Thailand, Italy and Iraq flights canceled. 

Lebanon Civil Aviation Authority
China, Korea, Iran, and Italy flights canceled for all non-Lebanese nationals and residents. 

Lufthansa
Mainland China flights suspended; 25 percent of all flights canceled.

Oman Civil Aviation Authority
Iran flights suspended. 

Pakistan Civil Aviation Authority
Iran flights suspended. 

Qatar Airways
Mainland China flights suspended, quarantining travelers from South Korea and Iran. 

Royal Jordanian Airlines
Flights between Amman and Rome suspended.

Saudia
Mainland China flights suspended.

Saudi Arabia
All Umrah travelers canceled, all tourist visas from Afghanistan, Azerbaijan, China, Hong Kong, Indonesia, Iran, Italy, Japan, Kazakhstan, Macua, Malaysia, Pakistan, Philippines, Singapore, Somalia, South Korea, Syria, Taiwan, Thailand, Uzbekistan, Vietnam, Yemen canceled.

UAE
All UAE citizens banned from travel to Iran and Thailand. 

United Airlines
Mainland China flights suspended, cutting flights to Japan and South Korea.

Virgin Atlantic
Suspended flights to Shanghai.

With agencies