In fact, they do take over the world, by measure of being the only ones left.
In It's Only A Paper World, when Brain is running short on fresh ideas, he comes up with a plan to create a scale-model replica of the world, using Paper Mache and Chia Grass. To convince people to move to this new world, leaving the original unoccupied and open for takeover, he offers them free T-shirts.
This plan actually works, and everyone moves to Chia World, leaving Pinky and The Brain technically the rulers of the original world, by dint of no one else being there.
Ending of episode below:
It ends when, irony of all ironies, the original world is completely destroyed by a meteor, forcing Pinky and The Brian to retreat to their duplicate Chia World, upon which their new world conquest plans take place.
It was a rather silly episode, but we DO get to see a few things The Brain would do if he took over, albeit with no one around to actually rule over besides Pinky.
There's also an episode of Freakazoid!, where meddling with the past causes Pinky and The Brain to be rulers of the world in the present as an end-episode gag, but I have no idea what episode that was.