YES! U.S. Citizens can still travel legally to Cuba under one of the 11 general licenses approved by the Office of Foreign Assets Control (OFAC). These licenses include support for the Cuban people, family visits, travel for university groups, academic research, journalism, and professional meetings. The full list is included below.

The two main changes apply to travel by specific types of vessels and to one of the general licenses under which to travel. As of June 5, 2019 travel to Cuba by “passenger and recreational vessels” is banned. This includes cruise ships and yachts, as well as private and corporate planes traveling to Cuba (Business Insider).
The general license “People to people” for group educational and cultural trips is no longer allowed by the OFAC.

The new regulations are in effect as of June 5, 2019.

The Treasury Department in a statement clarified that "certain group people-to-people educational travel that previously was authorized will continue to be authorized where the traveler had already completed at least one travel-related transaction (such as purchasing a flight or reserving accommodation) prior to June 5, 2019."
(CNN.com)

Americans can still travel to Cuba on commercial flights. It is allowed to engage in travel transactions such as purchasing a flight, reserving accommodations, and participating in a full-time schedule of activities as part of a program that complies with OFAC regulations.