Which form is the most correct?
No trabajo, soy jubilado.
or
Yo no trabajo, estoy retirado.
I'm not a native speaker, so feel free to skip this and wait for the comments of others, but here's my opinion:
First, the verb may depend on the country; I've only heard jubilado, but the Spanish I'm accustomed to hearing is that spoken in Argentina.
"No trabajo, soy jubilado" is correct, but I would interpret it to mean "I don't work, I'm a retiree" rather than "I don't work, I'm retired." To describe myself as being retired, I would say "No trabajo, estoy jubilado."
"Yo" is unnecessary in your second example, but not incorrect. I can only imagine using it myself if I were in a group where each person is describing his or her work, and my turn to speak followed that of several other people who were all employed. I might use "yo" as you did, but I'd probably emphasize it to call attention to the fact that my situation was different from those just described.
I hope that a native speaker will correct me if I'm wrong.

I too only know the word jubilado+, so I typed "I am retired" into Google translate and got +estoy jubilado.
Now I need someone to explain why it is estoy+ rather than +soy since being retired is not a temporary state.
Estar is used for a lot of situations that are what we think of as permanent, bjd. I don't remember the explanation that my teacher gave, but even "married" can take that verb. To our ears it would sound as if someone is about ready to divorce, but she said that in her experience estar was used at least as often as ser.
Retirado and jubilado are often used interchangeably but have different meanings:
Jubilado means that you are retired on a pension (from your former employer). A synonym of jubilado is pensionado (both jubilación+ and +pensión mean pension in Spanish.)
Retirado just means that you don't work anymore but without any implication of receiving a pension. So for example, if you are a freelancer or a shop owner, and retire on your own savings, you would be a retirado but not a jubilado.
I believe this also indirectly explains bjd's question about estoy and ser; I hope this makes sense.
Edited by: INSERSO to fix typos
I believe this also explains bjd's question about estoy and ser; I hope this makes sense.
I don't see the connection, but thanks for the three paragraphs that preceded that sentence. It's good to have a native speaker explain something that we foreigners are in a muddle about.