I've also heard some schools say that if your GPA is above a certain score, they don't even care if you take the GRE, but I doubt those are good schools.
Seeing as how I am very ignorant to how the GRE works... is this a must for most graduate programs?
It depends... there isn't really a "rule" for these things. The GRE, especially the general, is not useful in the very most selective programs. It just can't test a lot, and what it does test is somewhat irrelevant. (For example, the level of math is well below what most science students are used to, and whether someone can do these questions a few seconds faster, and with less chance of making a careless mistake, is not a predictor of success in graduate school). I think most of the best schools are aware of this, and some don't even require the GRE for certain programs. (e.g. I believe MIT doesn't for some quite selective programs). I see it as more of filter in the cases where there is a huge volume of applications.
However, in general, if you are applying to a Math (e.g. dept of mathematics) or Physics graduate program in the US, you will likely need both the GRE general and the GRE subject test. (Also, the GRE subject test in Math, unlike the general, is actually quite hard). And usually, if you are applying to US schools for Computer Science, you will need the GRE general. I'm not sure about engineering. I would guess that it varies a lot from school to school. IF the program you're interested in requires the GRE, and it is known as a selective school, I would say 750/800 on Math, 600 on verbal, and 5/6 on writing, minimum.
Also, studying/practice can make a profound difference on this test.