So I understand that there are factors that validate insurgent success, such as whether insurgents have safety, their ability to receive support from state or non-state actors, and if they are able to get strength from local government. But I was curious if Vietnam or Algeria could be considered a good example of insurgent success.
It really, really depends. For example, what do you deem a 'succesful insurgency'? A victory for the insurgents? Then certainly, both Algeria and Vietnam would qualify as a succesful insurgency. This is in as much as they achieved what they set out to do: Revolution, independence etc.
But do you mean succesful insurgency in military terms? If so, what sort of warfare are we talking about? If we're speaking about guerrilla warfare, then no. The Vietnam War would be a highly unconventional example in my opinion since it's very fluid between guerrilla, semi-conventional and conventional warfare - including forces that fought as conventional units and even conventional offensives several times during the war. If we deem the end of the Vietnam War to be the fall of Saigon then it would be easy to say that no, the insurgents did not win because the capital fell to a conventional invasion not fought by guerrilla soldiers.
The Algerian War would not be a good military example, since the FLN's military capacity by the end of the war was very limited. The war itself was far more guerrilla based than the Vietnam War, but the war was not won by military means but by political means. That in turn could definitely make the Algerian War be seen as a political insurgent success, but not a military.
So, as you can see, it's quite subjective in the end and you can turn it and twist it as much as you want, but there are many answers to that question.