To what degree were counterinsurgency operations by US forces during the Vietnam War successful?
In terms of the individual operations, they were quite successful on most occasions. I often read primary source accounts by soldiers and commanders in that conflict that suggest their frustration at winning nearly every battle, but being unable to win the war itself.
American counterinsurgency tactics developed and improved over the nine years of the war, applying the lessons learned at a huge cost in blood and treasure. American military commanders became experts at bringing superior force to bear, using air power and artillery to the utmost effectiveness, and fighting the Vietcong using multiple methods of counterinsurgency tactics. Supply interdiction, search and destroy missions and methods, detection and neutralization of tunnel networks, and especially Long Range Reconnaissance Patrols (LRRPs or "Lurps") and the intelligence they gathered were all particularly effective.
One of the best books I have ever read on the subject is About Face, by Col. David Hackworth. He wrote the Vietnam Primer during his repeated tours there, and About Face is his autobiography.
All of this being said, American forces were not able to choke off supplies to rebel forces, were not able to prevent large numbers of NVA regular army troops from entering the South, were not able to deny the rebels sanctuary, and were not able to win the hearts and minds of the civilian population, at least, not to the degree that it would turn the tide. Individual battlefield and tactical successes alone were not enough to win the war.