I'll add to Richard's contemporary answer and add that we have plenty of evidence for subducted plates in the geological past.
The evidence lies in the form of ophiolites. Ophiolites are fossil fragments of oceanic lithosphere, that for some reason (which I will not go over in detail here), survive subduction and become obducted (a fancy antonym for subduction) and emplaced on the surface. They are mineralogically and structurally distinct from anything that might find on "normal" continental crust. There are all kinds of ophiolites, and most importantly for our discussion are the SSZ (supra-subuction zone) ophiolites.
Let's look on the geographical distributions of ophiolites:
You can see that they are distributed all over the Earth. Some are obvious, such as the ones near New Zealand, because they occur on top of a convergent boundary (i.e. a subduction zone). Some are less obvious, for instance the ophiolites in Russia's Ural that sits in the middle of the continent. What this ophiolite represents is the past occurrence of oceanic crust between the west and east Eurasian continental plate, which amalgamated owing to the subduction of that (now long gone) oceanic lithosphere. Here's an example of how it happens:
(sorry, no idea where this comes from)
So that piece of ocean between the continent and the continental fragment is subducted and lost forever, but you can see the remnant of it in the form of an ophiolite, represented by that sub-vertical thick black line.
Another example, closer to me, is the Arabian ophiolite. You can't see it in this scale but it's actually a series of ophiolites, so called "suture zones", where pieces of small continental crusts formed in an island arc settings get "glued" to the main continental crust.So on the one hand, you have the Alpine-Himalayan orogeny, closing the Tethys sea (of which the Mediterranean is a remnant), operating mostly in the Cenozoic (past ~65 million years), forming modern day ophiolites. On the other hand, not very far from there, you have remnants of past oceanic plates, embedded in the Proterozoic continental crust of the Arabian-Nubian shield (more than 600 million years ago). To complicate it even more, it is now being rifted, evident by the formation of the Red Sea. Geology is fun!