Depending on what part of the world, there are a few invasive orchids. In the Dominican Republic, one frequently observed orchid is the Philippine Ground Orchid, Spathiglottis plicata, which I have found even along mountain trails away from human habitations; another is the Monk Orchid, Eulophia maculata. In California, one can find Epipactis helleborine, of which Weedy Orchid is one of the common names.
All these are terrestrial orchids. My impression is that epiphytic orchids are less likely to become invasive.
Do terrestrial and ephytic orchids, as categories, differ in how desired they are by collecters?