You see this in Ghost in the Shell (bioroids), Appleseed (bioroids), Xenosaga (Realians), Mass Effect (Keepers), Halo (Huragok), Warhammer (Jokaro), StarCraft (Zerg and their Buildings), Blade Runner (Replicants), Star Trek (Species 8472 ships), Metroid (Metroids, Aurora units) as well as in the book All Tommorrows (Colonials, Modular people's technology).
Most of the time the emphasis is on alternate molecular chemistries that imitate the molecular machinery of carbon based life though rather than just whipping up regular carbon-based DNA to make something else. Most of the time it is also used in constructs so intelligent they are actual beings in their own right. Examples of "dumb" or "mindless" appliances are rarer.
Which brings up the issue that "machine" is poorly defined in your question. Is an android suddenly not an android just because you make it out of carbon based molecular chemistry instead of metal and wires? Is a being made of electronics and metal doomed to always being called a machine no matter how advanced, complex, capable, and intelligent it is? Is a synthetic carbon based microorganism designed to decompose oil not a machine just because it is carbon based? Are you not a machine just because you don't feel like you are a machine despite meeting all the criteria for one? Your body is essentially a machine built with carbon-based nanotechnology.
The thing is that it takes a lot of effort and time to make something from scratch at such a small scale (or at least design it, if things are self-building but that process could be slow too...look at how we grow) so you probably would not do it unless it was necessary for function or the machine was worth the effort. A fridge might not be worth the effort. A computer, android, or starship might be.