I work for a large land management agency, and we have this problem too. You can keep the files tiled by UTM zone if you want, but it makes layouts more complicated. If you do this you will also have to make sure that the tiles edgematch across UTM zones - more work if you make frequent changes! We use ArcGis, and it handles projections on the fly well as long as you have defined your projection (have a .prj file). The way I prefer to deal with this is to project vector data in geographic (latitude/longitude), and then define the projection of my .mxd on a project-by-project level to ensure that data lines up with any raster data that may not project on-the-fly as well. You can then match the .mxd projection to whatever the UTM zone is for the area of interest. There is no perfect answer for this - there are advantages and disadvantages to both ways, but this works the best for me.
Hope this helps.