There can be a fine line between accepted naturalised plants that we have come to consider "indigenous" and others that have become established, but which remain interlopers. Quite a few of the former are happily included in the main bulk of the list of plants in this website.
And there can also be a fine line between those that have got out of hand and are considered "invasive". These are discussed here : index.asp?pageid=732296
What are discussed here are the various plants that are interlopers, plants that have escaped from gardens by injudicious dumping or spreading of seeds by wildlife. Plants that have become established , but which are not a threat to native species.
This is a subject group that is probably infinite as it keeps growing. It is somewhat pointless trying to cover everything found, but a few examples are included here.