Yes. Some land mines have self-destruct mechanisms to limit post -conflict civilian casualties, but in terms of 'a button' you want to look at rocketry.

All Western space rockets have historically had a self-destruct mechanism, with radio controlled engine cut-off and shaped charges, etc, to cut open fuel tanks or solid rockets. Russian rockets tend not to as they have vast areas of uninhabited land down range of a launch, their safety features are more to do with crew escape. China now does use self destruct I believe, after one of their Long March rockets came down in an inhabited area. A bad way to learn.

Usually this self-destruct is commanded by the launch facility's Range Safety Officer if it strays outside safe parameters, for instance if it looks like it will leave the launch corridor. I believe that they use a button. Whether it is red with a big label I cannot say. They have been used on manned flights, for example during the Challenger disaster it became clear that the huge Solid Rocket Boosters were spiralling all over the sky so they were deliberately destroyed to prevent further casualties on the ground.

It is likely that their will always be a human RSO with a button as a back up but companies such as ATK and SpaceX are developing autonomous self-destruct mechanisms. SpaceX had to use theirs last August when their F-9R Dev test vehicle 'experienced a flight anomaly' and unzipped itself with a shaped charge.

The first self-destruct button might be a question that is hard to answer. However, self-destruct buttons are a real thing. Radio self-destruct commands were and are commonly used in rocket testing because it's better to blow up a rocket at high altitude than it is to have a container full of rocket fuel falling back to earth at high velocity potentially over populated areas, enemy territory, or international waters.

Also, in general, it's been common military practice in the industrial age to attempt to destroy military equipment if it is likely to be captured. Warships get scuttled (and have design features to enable flooding, or explosive scuttling charges) Armored vehicles are destroyed if they can't retreat and so forth.