Reordering fields (permanently) in file geodatabase using ArcGIS Desktop?

In answer to another question I said that it is possible to use Summary Statistics to do the equivalent of PULLITEMS (old speak for reorder fields). That technique works well on Tables only but there is another script available now that says it works on both feature classes and table.

I would also recommend the Answer to Re-ordering fields permanently using ArcGIS Make Query Table tool? which was inspired by @klewis' Answer to this one.

The free version of ET Geowizards will do this. Basic -> Sort shapes. I just tested it on a v10 File Geodatabase and it works. It has to create a new feature class though.

As mentioned in the comments you can reorder fields with ArcGIS Diagrammer. I posted a more general step by step in this answer: How to update the length property of a feature class field?