In the short term, the attacks were good for US relations with other countries. There was much more sympathy for the United States. Many other countries felt that the threat of terrorism was a danger to them as well as to the United States. Even Iran reached out to some degree to the US in the days after the attacks.
In the long term, however, the effects have been less benign. The War on Terror has had negative impacts on US relations with various countries. More Muslim countries are more suspicious of the US because of things like drone attacks on their soil. Because the US has to be more aggressive in its pursuit of terrorists, it has hardened attitudes against it in some countries.