Can I get admission into abroad colleges without exams?

Honestly speaking, you would require one or the other exam to study abroad as 95% of the Universities require specific important exams like GRE, GMAT, IELTS/ TOEFL, and Bachelor's in a course related to the program you want to apply. However, you can waive off one or the other exam according to the University's eligibility criteria and the course you want to take.

Here is a list of Universities waiving off the GRE this year - 

Clayton State University
the University of Toronto
Syracuse University (optional but advised)
Northeastern University (optional but advised)
The University of Texas Austin (optional but advised)
the University of Washington – Seattle
the University of Minnesota
 New York University
Texas A&M University
Illinois Institute of Technology (not for PhD students)
Mississippi State University

List of Universities not requiring IELTS (USA) -

Rice University
Drexel University
Northwood University
University of Dayton
University of New Orleans 

I hope it was helpful. Let me know the country and the course you are targeting to get more information.