I guess if your definition is an operating railroad without a direct rail connection to the general system, there should be a bunch even leaving out the trolley lines. Many tourist lines fit the bill plus the Black Mesa coal line mentioned above. You can probably call a line "island" if the only connection is by water or road requiring transload. Some of the bigger ones like that might include:

* Alaska (though maybe they're a gray area because they do move cars in interchange using barges from Seattle).
* A couple of lines in Quebec N. Shore & Labrador - [www.sinfin.net]
* Several ore-haulers in Australia.

* Don't forget Cal Western in California - the Skunk Train - isolated by lack of NWP service for so long that the freight purpose of the line went away. Though I guess technically NWP hasn't been abandoned so Cal Western might not really qualify.

* And of course there are the lines that are on islands - like the one known by most fans as the E&N but now calling itself the Southern Railway of Vancouver Island (SVI) - [en.wikipedia.org]. Like Alaska, probably in a gray area because they can interchange cars with the mainland by barge.