Does a student who graduated from a lower-ranking school in a developing country be admitted to a graduate school in a western country? Most colleges in developing countries are sub-par by western academic standards. In one developing country, for example, professors are not obliged by law or by their institutions to pursue a doctoral degree. Even worse, this country’s state colleges lack decent science and computer laboratories, affecting in turn the quality of learning experience. No doubt, higher institutions in improvised countries have much to invest in their facilities, research, and faculty.

Having said this, does a student who graduated from a lower-ranking university in a developing country have a chance to be admitted to a graduate school in a western country? Based on your experience, do graduate schools give much weight to the reputation of your undergraduate school?  If your school is accredited in your country, will this help?
There is a chance, but it is not easy, unfortunately.  We get a good number of such applications at my department, and the problem is that we have no context to evaulate what the transcript means or what standards are used in the recommendation letters.  (In fact, often the letter writers do not seem to know how to write useful letters.)

As a result, you will probably need to do something else to (i) make sure you are prepared for serious graduate studies, and (ii) show that you are prepared for serious graduate studies.  For instance, study some serious books and write notes on topics online, or get actively involved in an SE site in your discipline.  If you can arrange to do something like an independent study with someone, or study abroad, at a reputable institution, that's even better as you can get a meaningful reference.

When you do apply for grad schools, say if you want to get a PhD from a good school it is probably easier to try to do a masters' degree at decent but not top school first, then try move onto a PhD program at a better institution.

See also the related question: How handicapped am I in graduate admissions if I graduated from a lower tier university?

PS I doubt if the admissions committee will have any idea whether a random school from your country is accredited or not, but if it's not, there's even less of a chance it will have prepared you for grad school.