There is nothing specific about green. Chlorophyll A and Chlorophyll B have different absorption spectrums. Depending on the specific combination of those two, the plants can appear in a different colours.
There are other pigments that cannot photosynthesise on their own, but can pass the energy to chlorophyll to react, as well. So while green usually means photosynthesis, absence of green does not mean absence thereof.
What other plants are there? Photosynthesis is performed in/by chlorophyll which is green, so it's hard to not be green.
There is a puprle earth hypothesis and Haloarchaea, which is based on witamin A related molecule for photosythesis, but those are not classified as plants.
The current theory for inception of plants is that one cell captured another chlorophyllic one and created symbiotic organism, which later evolved into multicelluar plants. So by definition plants should be green for phototrophy ("feeding on light"), until it would somehow evolved chlorophyllic cells, but ot seems they are older than plantae themselves.
Btw. similar theory exists for mitochondria and eukaryota, that's why we speak of my mitochondrial DNA.
A few plants are parasitic on other organisms, and have given up photosynthesis. An example is the Bird's-Nest Orchid (https://en.wikipedia.org/wiki/Neottia_nidus-avis) which is parasitic on a woodland fungus.
But these examples are unusual; the vast majority of plants get their energy the normal way, through photosynthesis using cholorophyll.
