Can I get a letter of recommendation from a professor who didn't teach me BUT I did research with? I am an undergraduate student wanting to transfer to another institution for undergraduate studies. I am a research assistant for a professor at an institution that I do not attend.

Would the university which I which to transfer to, accept the recommendation letter from this professor? Again, I have not taken any courses with this professor, nor go to the institution where he teaches.

Related (except for Graduate Admissions): Copied Letter of Recommendation?
The point of a letter of recommendation is for the receiving party to obtain third-party verification that you are, indeed, awesome. Generally speaking, people like to receive letters from individuals who know you well professionally. In most cases, teachers cannot write good letters, as they only know you as a face in the class, and never really got to know your work ethic, personality, and capabilities. A research advisor would be able to comment on all those things, and would be able to write a much stronger letter.