While not a true lime, the Rangpur lime is highly acidic and is a wonderful substitute for regular limes due to its lime-like zestiness and its orange-like juiciness. The flavor of the lime is said to taste a little bit smoky.
Originally from India, the Rangpur lime found its way to the US in the 19th century. The gin company Tanqueray has a Rangpur-infused gin called Tanqueray Rangpur. Rangpur lime trees are popular as ornamental trees, but the fruit is also great for cocktails, lime curd, ceviche, guacamole, and any recipe calling for lemon or lime juice. Zingerman's sells a wonderful rangpur lime syrup.
(Image: Flickr user m.paoletti - thanks!)