I am relatively familiar with this for domestic (US) students, but less familiar with the requirements for international students. I'll assume the requirements are the same....
Have you done any research at all, even for a big class project or something on your own? If so, mention these. The admissions committee that reviews your application will want to know that you're interested in doing research and that you know what you're getting yourself in to.
If you have a couple years left before you graduate, I would try hard to get a research experience before you apply, even if you have to volunteer (work for free) for a semester. If I had to make a guess, I'd guess that most programs would want to see that you have done at least one or two research experiences, if only so that they know that you know what research is.
Formal research experiences (summer research internships, for example) and publishing a paper or two are great, but they're not the only criteria.
First, it depends on how competitive the program you are applying to is. More research experience may be needed to help you stand out enough to be accepted. Publications are always great, but research experience (which may not have resulted in a publication) is still well-regarded.
Another factor grad programs consider is how focused you are, and if you have an existing connection with a research group in that program. For example, you may have previously collaborated with a professor in their program, and he/she is familiar with your work. If you show a genuine interest in working with him/her, it will reflect well on you, and who knows -- he/she may be able to help your application get accepted. If you just want to get accepted into their program, but it looks like you have no direction or research interests after that, the committee reviewing your application will look less favorably on you.
Lastly, when you apply, you should apply for a spread of schools. Apply to 1-2 competitive programs which, if they accepted you, would make you feel lucky because you weren't sure you qualified. You should apply to several programs that you think might accept you. Lastly, apply to a few programs which you are certain you would be accepted to, just in case you aren't accepted to any of the others.