Most graduate departments have a minimum GPA cutoff. If you don't make it, it's tough bananas.
In some cases you will have an opportunity to cite extenuating circumstances, but usually these are more for situations like "I took time off from school that year to help my family escape a genocide" or "I didn't manage to hand in every assignment due to my chemotherapy sessions" rather than "my girlfriend broke up with me and I spent my semmester playing video games rather than studying."
And you also have to be able to demonstrate that you have the potential to succeed as a graduate student. For example if you had a couple crappy years, but then found your true interest and have been able to maintain a high average in senior courses, then you have a lot better shot than having done mediocre all the way through.
Also, just because your university has a high assignment on a more-or-less arbitraty index index, don't count on that doing a hole lot for you. It might be given additional weight in some places, under some circumstance, but don't count on that.