I will start by saying that your question contains a contradiction:
EDIT: I want my program to be really robust, ... The thing I really want to avoid is a program termination even at the cost of some corrupted state.
A program that keeps on limpin' in case of corrupted state isn't robust, it's a liability.
Second, an opinion of sorts. Regarding:
EDIT: I want my program to be really robust, even against programming errors. ...
When, by programming errors you mean all bugs, then this is impossible.
If by programming errors you mean: "programmer misused some API and I want error messages instead of a crash, then write all code with double checks built in: For example, always check all pointers for NULL before usage, even if "they cannot be NULL if the programmer didn't make a mistake", etc. (Oh, you might also consider not using C++ ;-)
But IMHO, some amount of program-crashing-no-matter-what bugs will have to be accepted in any C++ application. (Unless it's trivial or you test the hell out of it for military or medical use (even then ...).)
Others already mentioned SEH -- it's a "simple" matter of __try / __catch
.
Maybe instead of trying to catch bugs inside the program, you could try to become friends with Windows Error Reporting (WER) -- I never pulled this, but as far as I understand, you can completely customize it via the OutOfProcessException...
callback functions.