Do I need passport for US domestic flights, due to the 2019 REAL ID requirements?

Update April 29, 2021:

The deadline has again been extended, this time to May 3, 2023. Thanks to user102008 for bringing this to my attention.

Update March 27, 2020:

To reduce the need for people to go to DMV offices during the coronavirus pandemic, the deadline of October 1, 2020 has been postponed until October 1, 2021. Thanks to choster for linking to an initial report by Bloomberg News.

Several news organizations have been reporting the new deadline at least since yesterday evening. An official press release from the acting Secretary of Homeland Security is dated yesterday, March 26 2020.

The page quoted below has now been updated, as have the quotes themselves. I've also adjusted the answer to account for the fact that Pennsylvania is now compliant with Real ID rather than being on an extension.

Have a look at https://www.dhs.gov/real-id-public-faqs:

Q: When will I need to change how I travel domestically?

Beginning May 3, 2023 every state and territory resident will need to present a REAL ID compliant license/ID, or another acceptable form of identification, for accessing federal facilities, entering nuclear power plants, and boarding commercial aircraft. The card, itself, must be REAL ID compliant unless the resident is using an alternative acceptable document such as a passport or passport card, or state-issued Enhanced Driver’s License. The Act does not require individuals to present identification where it is not currently required to access a federal facility (such as to enter the public areas of the Smithsonian) nor does it prohibit an agency from accepting other forms of identity documents (such as a U.S. passport or passport card).

You can use a Pennsylvania-issued document (license or ID card), even if the document is not compliant, through May 2, 2023. After that, you'd need a compliant document or one issued by the federal government (for example, a passport or passport card).

Is Pennsylvania compliant? Does it have an extension? See the main Real ID page at https://www.dhs.gov/real-id, which shows a map indicating that Pennsylvania is compliant. You can choose Pennsylvania in the "select a state" box below the map to see the details:

Pennsylvania is compliant with the REAL ID Act. Federal agencies can accept driver's licenses and identification cards from Pennsylvania at Federal facilities and nuclear power plants.

On or after May 3, 2023, you'll need a Real-ID-compliant driver's license or your passport (or another document from the TSA list, if you have one).

No, but soon you will need to update your drivers license to a READ ID compliant one

Beginning Oct. 1, 2020 2021, if you plan to use your state-issued ID or license to fly within the U.S., make sure it is REAL ID compliant. If you are not sure if your ID complies with REAL ID, check with your state department of motor vehicles.

Pennsylvania does have a REAL ID drivers license. Your passport is also an acceptable REAL ID identification, but it is not required for domestic flights.