What has been the effect of the 9/11 attacks on American relations with other countries?
In the long run, the attacks have made America's relations with other countries more problematic.
After the attacks, the US invaded Afghanistan and, later, Iraq. These conflicts have made US relations with many other countries more difficult. First, they have helped to weaken US relations with Muslim countries. Though we in the US would not agree with them, many Muslims see US actions as attacks on their religion. This makes them less likely to have good relations with the US.
The US has experienced some difficulties with non-Muslim countries as well. For example, the US has had to try to hold together coalitions to help it fight the wars in Iraq and (now that that war is over) Afghanistan. This has led to some strains with other countries. The continuing US commitment of troops in Afghanistan, and the strain the US military has been under, has also made it harder to credibly threaten some other countries such as Iran. In general, the focus on the Middle East after 9/11 has also reduced America's ability to focus on other issues such as the rise of China.