Is music from the 60s and 70s still copyrighted?

The answer depends on whether you mean sheet music or recorded music; they each have their own copyright and expiration. One may expire without affecting the other.

More than likely, yes. In general a US copyright is valid for the life of the holder plus 70 years, or 95 years from publication, if done as a work for hire.

However, the duration of a particular copyright can get complicated in the area of "music" and "sound recordings" of music that happened to occur in the 1960s and 1970s.

First, consider that federal copyright does not include any sound recordings made prior to 1972. State laws, however, cover sound recordings and those laws do not have any expiration (unlike federal copyright), at least not until pre-empted by federal copyright law in 2067. Thus, you must consider ALL pre-1972 sound recordings to be copyrighted until then.

On the other hand, the underlying "music", as a composition of notes (and maybe lyrics), may or may not be protected, depending upon when it was created or published, and if a renewal was filed. A related answer addresses the question of copyright duration in more detail.

See the Related Link, "Wikipedia: Copyright" for more information on copyrights.