The capybara is the current champion for rodents of unusual size — it weighs about 60kg (about 130 pounds); another large rodent is the pakarana, which weighs about a quarter of that. Either one is far too much rattiness for most people to want hanging around.
Now there’s another king of the rodents: Josephoartigasia monesi, which is estimated to have tipped the scales at about 1000kg, over a ton. Don’t worry about getting bigger rat traps; these beasties have been extinct for perhaps 2 million years. I’ve put a few pictures from the paper describing this new species below the fold.