Have any genetically altered organisms actually become abundant in a natural environment?
Many organisms including plants, bacteria, insects, fishes and even mammals have been GMed. Most of them have experimental purposes, but GM crops have been released for commercial purposes. Maybe the most amazing between them is triticale, which is a hybrid of wheat (Triticum) and rye (Secale). Triticale, BT Potato, BT Tomato, BT Maize (I am not sure), BT and Golden Rice and lots of other GM crops have been released in almost all lands in world. Almost all these GM crops suppose to have higher yield and higher resistance to pathogens and physiological problems and as a result they have higher chance of surviving (specially in natural environment). 
A study published in Nature in 2001 reported that Bt-containing maize genes were found in maize in its center of origin, Oaxaca, Mexico. In 2002 Nature concluded that the evidence available is not sufficient to justify the publication of the original paper.  A significant controversy happened over the paper and Nature's unprecedented notice. Also there are safety concerns about modified gene transfer during pollination in GM Rice(s). Even some scientists think that that this would not be a problem because rice is a self-pollinating plant. Any way GM crops can become abundant and release their genes by themselves or through gene transfer to other organisms.