Do You Need Morse Code for a Ham Radio License?

No. In the US you don't need Morse code for any amateur radio license. The FCC removed the Morse code exam for every license class effective February 23, 2007.

What changed

The Technician license dropped its code test back in 1990. General and Amateur Extra still required a 5 WPM test until the FCC adopted a Report and Order in WT Docket 05-235 on December 15, 2006. The FCC said the test could discourage hams from advancing their skills, and it dropped the requirement for both classes, even though the ARRL had asked to keep it for Extra. The ARRL reported the new rules took effect February 23, 2007.

The change followed the ITU's 2003 World Radiocommunication Conference, which let each country decide whether to require Morse for HF access. Outside the US, check with your national regulator.

Today, all three US license exams are written, multiple-choice tests.

Why many hams still learn it

It gets through. A narrow CW signal stays readable when voice is lost in noise, so low power and simple antennas can reach other continents.
Simple gear. CW rigs are small, cheap and popular for portable operating.
The challenge. Plenty of hams enjoy CW the way people enjoy playing an instrument.

If you're curious where CW lives on the bands, see what frequency Morse code uses. To start learning, follow the plan in how to learn Morse code and practice in the trainer.