As the other posters above point out, it does depend on your point of view. Militarily, it was an almost unqualified success. Estimates range from 30,000 to 68,000 Vietcong killed in the offensive, with up to 100,000 wounded. This decimated most of the mainline VC units, and Vietcong activity in the Mekong Delta and elsewhere dropped significantly after this offensive failed to cause a popular uprising or the ARVN (South Vietnam's Army) to collapse.
However, it was a public relations disaster. Americans shifted against the war such that it became impossible for LBJ to continue, or for another President to get elected without a plan for us to leave Vietnam.
Although the South Vietnamese and American forces were taken by surprise by the massive surprise attacks by the Viet Cong forces, they were eventually able to contain them, inflicting massive casualties on the enemy troops. Nevertheless, the Tet Offensive that began on January 31, 1968 served notice to the United States that the North Vietnamese were capable of mounting a major strike backed by large numbers of troops.
The Tet Offensive was so named because it fell on the first day of the lunar new year (known as Tet Nguyen Dan)--Vietnam's most important holiday. The North Vietnamese initially gained the momentum since both sides had previously agreed to a two-day truce in honor of the holiday. The Viet Cong's first-day attacks struck in more than 100 locations utilizing at least 80,000 troops. American and South Vietnamese forces inflicted heavy losses (approximately 37,000 casualties) during the two months of the offensive's first phase. Tens of thousands of civilians were also killed or wounded.
The offensive, meant to disrupt South Vietnam and hopefully cause an uprising that would topple the Saigon government, involved the largest numbers of troops in the war up to that time. It was a strategic victory for South Vietnam and the U.S., but it also showed that the war was far from nearing its end.
This depends on how you define victory. Historians typically argue that the Tet Offensive was a tactical victory for the US but a strategic defeat. What that means is that the US won the actual fighting, but that the offensive hurt them in the bigger picture, allowing them to "win the battle but lose the war."
The US defeated the enemy all over the country in the Tet Offensive. It is said that the offensive hurt North Vietnam very badly. However, it hurt the US worse. The problem was that the US government had assured its people that the war was being won and the enemy could no longer do much in the way of resisting. When the Tet Offensive happened, it was clear that that was not true. This damaged the morale of the American populace and turned them more strongly against the war.
In these ways, the Tet Offensive was a tactical victory for the US, but ended up hurting them in the long run.
There were 2 battles in this Vietnam War, the conflict between south/north VN triggered the war in the battle between US vs China/Russia. The US decided to have a deal with China for pulling out to let them take over and letting the South Viet Nam to lose the war.
My father, a Lieutenant, was there in this battle witnessed how the US assigned most of all the South VN intelligence troops to another location, and we believe the US SOLD the info. to the North VN (China). The disadvantage of the US adapting to another battle field was another story, but to the South VN soldiers saw that they could take over the capital of VN, Ha Noi, at that time; however, the US had their own battle in control.
One more thing that the US stopped supplying and they didn't even loan the South VN the supplies to fight back when they left because they were afraid the South VN might win the war which they had the ability, and the deal between the US and China couldn't be done.
That's why you're seeing today, Made in China is nearly everywhere.