I've read that the cell nucleus was once an autonomous organism that was "enslaved" by the larger cell at the time of the Eukaryotic Revolution. Are there any organs in the human body that we know of that started out as autonomous organisms (of course they would be unrecognizable in their current form)?
Very short answer
It is not the nucleus who was an independent organism but the mitochdonrion (organelle) (One might discuss this point and say that both are correct it is just a point of view). The plastids (the chloroplasts for example) were also independent organism. In consequence, in every cell, we have DNA in the nucleus and DNA in the mitochondria. The mitochondria is contained in every cell of our body and is transmitted via the ovule (and not the spermatozoid) to the offsprings.
Now let's think about your hypothesis that one of our organ (let's say, our liver) might have been an independent organism in the past. Therefore, this organ would contain different DNA than the rest of the cells of our body. How would you transfer the DNA of your liver to your offspring? Well, it is hardly imaginable.
Moreover, it has been argued that because we now have a complex and efficient immune system, a endosymbiose would be very unlikely.
But no, none of the cell in our body come from a previously different organism. But every cell of our body is some kind of chimera of two previous cells. Note: the vast majority of our DNA are present in the nucleus and not in the mitochondrion.
It seems much more easy to have two organisms that stay together during reproduction when reproduction is mediated by striking.
You may find some funny examples (border cases) of two organisms that don't separate during reproduction in corals (zooxanthella), leafcutter ants (and their fungus), parasitoid bees (and the virus that females create in their ovary) and lichens
Remi.b is perfectly correct if the question were restricted to humans (and yes, nucleus is not thought to be a result of symbiogenesis; actually some bacteria have similar structures).
But in the animal kingdom there several cases when certain organs "start(ed) out" as more or less separate organisms: