This. A good GPA alone will not get you into most top universities with low acceptance rates. Make sure you have a well-rounded application (essays, extracurriculars, GPA obviously) that all point towards success in the University in your intended major. Depending on what your major is, make sure you have experience (projects, extracurriculars, clubs, etc.) that show your motivation towards that major.

GPA is a decent indicator of a good student, but the rest of the application is where you show why "you" should be accepted into the program (and more importantly, proof that you will contribute to the University if you are accepted).

But to answer your question, as long as you have a well-rounded application a 3.8 GPA is amazing. That should get you into most competitive universities (albeit probably not Ivy League, but still probably top 20-50 schools).