My academic paper had a pretty standard order, based on contribution: primary/thesis student (me), supporting/project student, supervising professor, technical advisor professor. I did most of the work and wrote the first draft based on discussions with our advisor (supervising professor), the other student added in her section and revised/tweaked my text as needed, and then I sent it over to the supervising professor and technical advisor professor for review, and we went around a bit to clean it up and force it into the correct format.
There was no disagreement (or even discussion, really) regarding the order of authorship on our paper. The project student and I were working on similar aspects of the same general research area under the same grant, so our work had been coordinated reasonably well from the beginning. My advisor and the technical professor were both
If I do write another paper, though, it will be as part of a team of near-equal contributors and a veritable army of support staff. I'm not a particularly fancy cook, but I like the idea of using a quasi-random method to determine authorship. Fantasy football, maybe?