How is it possible for them to have become organelles over time?
The main evidence I suppose behind the theory is that they have their own DNA and they resemble simpler organisms. How they came to actually live inside cells, no idea but considering how bacteria can make theuir way into our cells its not that difficult to imagine. The difference is, while bacteria are harmful to us, mitacondria have a mutualistic relationship with us, ie. a relationship that is beneficial to both parties.
I took Ap biology recently and they said that the mitochondria may have originally formed a coloial like relationship with another "prehistoric bacteria" and then over time the mitochondria became dependent and then included within the new more complex organism... if that made sense...