If you don't want a shape spinner (circular, square etc.), you can use shape morpher. I.e. design one shape to be beginning, and other shape to be the end, and the progress/activity can be be displayed as morphing. I didn't see such activity indicators used often.

Another idea is to use a 3D style indicator, but that should fit with 2D design well.



I like how WolframAlpha for example uses a miniature game of life as an activity indicator.