Shimano cassette
 

If you have removed the cogs off the cassette (ultegra), is it possible to install them backward. Meaning when they are factory fresh I believe the stamped numbers on the individual cogs (indicating # of teeth) are all pointing out towards the frame (not in towards the center on the hub). So is it possible to install some pointing in while others are pointing out? Or are they keyed (somehow) to prevent this??

It's possible, but don't. The spacing won't be correct.The stamped numbers on each cog should be facing you as you are installing the cassette. Note that some of the cogs have a shoulder on them that acts as a spacer for the next cog. The loose spacers fit on the outside of the cogs that don't have this shoulder (they are flat).

You can't put them on backwards because the spline pattern isn't symmetrical.

Not without grinding one of the tabs on the cogs (the wider one).

History note: You could flip Uniglide cogs (except those with built in spacers) since the splines were symmetrical. The tooth profile was also symmetrical so it worked the same either way. You could get twice the life out of a cassette!

Thanks. I just checked and all the numbers were facing me when they went back on (just like they were when they can off).