Yes. All of these I am suggesting are for PhD, not MA. (in the USA)
Ideal package
All of tuition and fees covered
Stipend for living expenses; >$22k in a high-cost-of-living city, >$17k in a mid-sized city, or >$14k in a small town
A year (or two) of fellowship, so that you have no duties grading in order to work on courses or dissertation
(Supplementary scholarship)
Funding for 5 years, with a potential for a 6th year of funding if necessary
Common package:
All of tuition covered, but not fees
Stipend for living expenses; >$20k in a high-cost-of-living city, >$15k in a mid-sized city, or >$12k in a small town
Funding for 5 years, with a potential for a 6th year of funding if necessary
Sub-par package:
>50% tuition covered, few to no fees covered XOR (exclusive or) healthy stipend for living expenses
Supplementary scholarship
Potential for full funding or extra work in the department
Avoid-me-like-the-plague package:
Must pay out of pocket
Tuition discounted less than 50% off
No stipend
As you can see, there's quite a range. Most are in the "common package" and deviate in some way or another from it.