Aside from the dyed, painted and similar coming from China that claim to gem materials (including so-called "Sea Sediment Jasper" that coincidently is hawked masquerading as everything from OJ to Biggs), there are also some that aren't even stone. Here is a tiny (small earring) cab I bought a decade-or-so ago as genuine "Owyhee Jasper" just to literally have a crack at it:
(http://i777.photobucket.com/albums/yy56/gemphoto12/jasp_owyf029.jpg) (http://i777.photobucket.com/albums/yy56/gemphoto12/jasp_owyf030.jpg)
Glass substrate with fired-on, transfer-printed glaze from photos of real jasper. Similar weight, slight translucency, RI, glassy surface and conchoidal fracture as good jasper, but looking under magnification with directional lighting as in the photo, you can see the web pattern from the printing. I expect they've improved that with better technology in the years since. Immediate tip-off to me when looking online was that both earrings had the exact same pattern (not even bookmatched), though that clumsy misstep could have been by now also be addressed by more astute sellers. These fakes using patterns derived from genuine stone have been sold in various popular standard cabochon sizes, some more difficult to detect and more detailed (esp. in the larger pieces) than this one.