It's about 0% for sub-Sahara Africans, and in the 1% to 4% range for the rest. [1]

This may not mean exactly what you think it means though. Your non-Neanderthal genes are also almost identical to the Neanderthal ones, otherwise interbreeding would have been impossible. It's just that genes come with slight variances that can be used to trace ancestry.

E.g. you may also have heard that humans and chimpansee DNA is 98.8% identical, so there is obviously a different type of similarity metric being used there

[1] https://www.science.org/doi/10.1126/science.1245938

Some of the very similar Neanderthal variants of genes are manifest as important phenotypic differences though. Traits ranging from hair straightness, sneezing after dark chocolate, to severe COVID risk. Some alleles are now suddenly quite deleterious due to modern lifestyles, like the CHRN3 gene variant, but wasn't before widespread smoking.