This is, of course, a matter of opinion. There is no objectively correct answer to this question. My own view is that only the 14th Amendment is still relevant. However, many people would argue that the 15th Amendment is as well.
I do not think the 13th Amendment has any relevance today. There is no one who would seriously argue that we would be in danger of having the institution of slavery reappear in the US if the 13th Amendment were not part of the Constitution. This was an important amendment when it was written, but it is no longer important.
I also do not think that there are many people who are interested in depriving people of the right to vote because of race. It may be true that Republicans are pushing bills that might end up reducing the number of minorities who vote (picture ID laws, for example), but I believe that they are typically doing this for partisan reasons. I think they are trying to deprive people of the right to vote because they are Democrats, not because they are non-white.
The 14th Amendment, however, remains important. It is important mainly because it applies to people other than African Americans. I do not think the government is seriously interested in reinstituting segregation. However, I do think the 14th Amendment remains important for such things as gay rights.
I would argue that most rights of non-whites are no longer in danger from the government. Therefore, I think that these amendments are not as important as they once were.