I think it was Whitney who asked a question about the relationship between basalt rock and granite rock. It turns out that this is key to understanding which plate 'wins' when they collide. Basalt rock is heavier and granite is lighter. Plates made of basalt tend to be forced under the lighter granite plates. The lighter granite plates form the continents. Basalt and granite are addressed here at the Ask a Geologist page. The analogy seems backwards though - the heavier truck ends up on top of the lighter VW whereas the heavier basaltic plate ends up underneath the lighter granitic plate.
As it turns out, most of the ocean floor is basalt, and most of the continents are granite. Basaltic crust is dark and thin and heavy, while granite is light and accumulates into continent-sized rafts which bob about like corks in this "sea of basalt." When a continent runs into a piece of seafloor, it's much like a Mac truck running into a Volkswagon. Not very pretty, but at least there's a clear winner. And the seafloor basalt ends up in pretty much the same position as does the VW - under the truck (or continent, as the case may be). This may seem like a drag for the basalt, but remember that it isn't all that happy on the surface anyway, and this gives it the heat it needs to re-melt and try to complete the differentiation process which was so rudely interrupted at the spreading ridge. If successful and allowed to continue, what's left behind is a "purified" magma with most of the iron, magnesium, and other heavy elements removed. When it cools, guess what forms? And the continental land mass just got a wee bit larger.
The following YouTube video from National Geographic is a little dramatic and they fail to mention now speculative the positions of the early continents are but even so I thought I'd post it because it nicely covers several topics we looked at from the bombardment of the earth, to the origin of life, to the production of heat via radioactivity and the movement of the plates.