How I Use It
1. My students used it as their standard grapher in addition to their TI 84 calculators. The precision and ease of use of a desktop software meant that students spent less time trying to wrestle with UI or fiddle with tiny zoom windows and more time actually doing math.
2. I used GeoGebra quite a bit for projects involving analyzing graphs and numbers at the same time. It takes about two minutes to build a demo for something like finding limits of a rational function in GeoGebra, and it's also very easy for students to make their own. The geometry, the algebra, and sometimes the data is simply displayed side by side, which helps students really see the connections between them.
3. GeoGebra is also great for inquiry based learning. I've done lots of exploratory exercises in my calculus classes using GeoGebra and it's great for kids to be able to see relationships between secant lines and slopes and functions all change as they move points around. It also allows students to explore the connection between data and functions via plotting points from the spreadsheet and playing with them.
4. GeoGebra isn't a full statistics or spreadsheet package, so there are things that it wasn't able to do for some more specialized classes like statistics. However for courses from algebra 1 to calculus it was more than sufficient.
I used GeoGebra extensively at my previous school. My department adapted it as a replacement for Geometers Sketchpad since GeoGebra is cheaper (free), does much more, and was easier for our IT team to manage. It also replaced Excel / other spreadsheet programs for classroom use for our precalculus, calculus, and statistics courses since GeoGebra has extensive spreadsheet capabilities that tie into the geometry and algebra. Added function aside, having one software instead of several streamlined everything both in terms of teacher and student training. Ultimately, using GeoGebra instead of GSP and Mathematica (which was what we used for visualizations and graphing before GeoGebra) saved us around $2000 per year in licensing fees.
The biggest problem I had with GeoGebra (as well as one of its strengths) is that it's Java based. This meant that Java errors or students who didn't update their devices regularly sometimes had problems. It also ran slow on some of our netbooks. It also didn't have Vernier probe connection capabilities so it meant that we had to do some extra steps via Vernier's software if we wanted to gather data, but that was not a major issue and can be forgiven easily since GeoGebra is free.