I know this question is raised quite frequently, but I really have tried to display my rasters (TIFFs) in every combination of resampling/pyramids/colormap I can think of and nothing seems to help. In this attached screen shot you see the raster on the left in ArcMap and the raster on the right in a plain photo viewer. I do see a *slight* improvement when I use bilinear or cubic instead of nearest, but it isn't enough. I've rebuilt pyramids using all the different environmental settings and have tried importing the rasters in different ways. They always show up shoddy.
Do you have a stretch applied to the raster? If the stretch is set to 'Standard Deviations', try changing it to 'None' and see if this helps. You can change this in the Properties > Symbology tab, or use the new Image Analysis windows for ArcGIS 10.