I had thought that this question would be easy to answer but my searching has been unsuccessful in finding a clear answer.
For the metals, I expect that they all form oxides. Some very readily, e.g. sodium and magnesium, and some reluctantly, e.g. gold and platinum, but I cannot find a metal which does not form an oxide.
The metalloids also all appear to form oxides.
The noble gases are obvious candidates for exceptions but xenon has a known oxide. I think that it is expected for radon but I don't know whether that is confirmed. A fluoride is known for krypton but no oxide yet. No oxide is known or expected (?) for any of the lighter noble gases.
This leaves the other non-metal elements which are sufficiently few to check easily. I find no exception except for the possible pedantic case of fluorine. It forms a binary compound with oxygen but since it is more electronegative the compound is called oxygen fluoride rather than fluorine oxide.
Some elements are too radioactive to study e.g. francium and astatine but I expect that both would form oxides if we could manage to study them.
Edit: a good point that came up in the comments is oxygen itself. A pedantic exception together with fluorine.
Is that correct?