Someone told me that the Prophet once said that "nationalism and pride in one's culture is not right".  I was wondering whether the issue of being a Pakistani and having Pakistani culture can co-exist with being a Muslim.  In the time of the Prophet did people still stick to some of their cultural traditions or is all that abolished and not allowed?

Nationalism or Cultural affiliations are a natural phenomenon. Every one tends to have a sense of belongingness with the people of his society, his country, his region, his language, even his city. There is nothing wrong with this.

Nevertheless, when one's affiliation with some culture, or region creates a bias and prejudice in him, that hinders in one's submission to the Truth or when such bias or prejudice can influence one to leave a just stand and opt for injustice, such bias and prejudice become wrong and even condemnable.

In my opinion, this is what the saying of the Prophet (pbuh) means. Nationalism and cultural and even political affiliations, if kept within limits, have nothing un-Islamic about them. However, a true Muslim can never hold to the view: "My country, right or wrong". On the other hand, Islam teaches us to be just and truthful, be it against our own advantages, our country's advantages or the advantages of our loved ones. (In this regards, do have a look at Al-Nisaa 4: 135 and Al-Maaidah 5: 8.)