Yes. The vast majority of vaccine programs have herd immunity as their goal, either explicitly or implicitly.
Importantly, herd immunity is not an approach, it is an attribute of a population.
A population can be said to have reached herd immunity when enough members of that population are fully inoculated against a given disease so as to prevent a sustainable infectious spread (in other words the average number of people infected by a sick person is less than 1, resulting in the eventual die off of the pathogen).
By definition, vaccines are a herd immunity strategy. It is actually impossible to achieve a 100% vaccination rate, as there will never be a vaccine that is safely tolerated by every human on the planet. Instead, the goal is to reduce the number of candidate hosts for the pathogen by vaccinating as many people as possible (the target number for herd immunity varies by pathogen).
In some diseases, contraction of the disease (e.g. chickenpox) is an effective means to attain immunity. If the disease is generally low-risk (e.g. chickenpox), then it becomes feasible for exposure to be used as a means of achieving inoculation. For much of my childhood this was the de facto means by which chickenpox (for which there was not a readily available vaccine at the time) was confronted as a public health issue: invariably someone at a school would contract it, it would spread through the student body despite everyone's best efforts to avoid this, but since chickenpox infections during youth are generally low risk, everyone from parents to school officials on up shrugged their shoulders and considered this to be standard operating procedure.
Of late, there has been a misunderstanding of this strategy by the lay public, leading to things like "measles parties." The problem there being that measles is not a low-risk disease, it is quite often fatal. Public officials saying "just get the disease and get it over with" is an artefact of that recent social development rather than the understanding of herd immunity.