With the restriction of physicists after the year 1900, were there any self-taught physicists that achieved fame without having gone to university?
A similar question was asked to the theoretical physicist Gerald 't Hooft on his page 'Theoretical Physics as a Challenge'. It is mentioned at the bottom of the linked page:
Mr. Hisham Kotry came with an important question: "... Two years ago I decided to self-study theoretical physics by following the syllabus of a renown university and the advice from your page and now I'm half-way through the journey but I was wondering about what happens next? ...Do you know of anyone who got tenure at a physics department or any research institute based on studies he did in his own time without holding a university degree?"
T'Hooft quoted the following message from a contributor to answer a part of the question:
3/04/06: Message received from John Glasscock, Bloomington, IN: The only one I know of currently is John Moffatt at U Toronto, who was a student of Abdus Salam at Imperial College, London. He started life as a painter in Paris, had no undergraduate degree, taught himself, corresponded with Einstein, and was admitted, based on his demonstrated original work, at IC. (Source: Jo�o Magueijo, Faster than the Speed of Light. Perseus Publishing, Cambridge, MA. 2003.)
I'm not sure if the example I quoted satisfies the "famous" criteria you stated in your question, but I hope this helped!
The best example I can think of is George Green. George Green quit his studies at the age of 9 to work with his father and eventually was owner of a mill. He spent the majority of his life as a miller but found time to work on advanced math and developed concepts far ahead of his own time. He published an essay on electromagnetism in a little known journal that would eventually have a wide reaching impact in nearly every branch of physics. He is the namesake for Green's theorem and Green's function as well as some other important mathematical objects.
Eventually he did go to Cambridge at the age of 40 and earned his degree but this was well after his most important work. So it can be argued that he achieved this without going to university.
An interesting case to mention is Freeman Dyson. While he did earn a masters degree, he never earned a doctorate but was still able to work as a mathematical physicist. Many people, including Steven Weinberg, believe he should have been awarded a Nobel Prize for the work he's done.
I'm not sure if you count applied physics (aerodynamics) as well, but if you do, I have an answer. The Wright Brothers never finished high school and never went to university, and they invented their machine in 1905, so that is after 1900.