So you have watched the Rise/Dawn of the Planet of the Apes movies (yay!) or you are at least aware of their titles (go see them!) and, like I did at first, you think they got the naming backwards. This appears to be a very common thought when I talk to people about the Apes movies so I thought I would share an explanation. Very mild spoilers follow.
I see it as something must rise before it can dawn. Whatever is dawning was not static before it actually dawned, it had to do something to get to that point. An example would be if there were a mountain between you and a launching rocket. The rocket has to rise before it can dawn over the horizon you are witnessing.
Within the movies themselves, I think the titles are very appropriately chosen. In the first one the apes are rising from the captivity they have been placed in. Another way of looking at it, especially towards the end, is it's an uprising of the now intelligent apes. In the second film we are witnessing the dawn of a new era; An era where apes are now the dominant species.
(Image credit We Are Movie Geeks)