At ArcGIS 10.1, one can change field names for tables/feature classes in a 10.1 geodatabase. Field names must still conform to geodatabase field name guidelines and fields in a 9.3.x or prior release geodatabase cannot be renamed. Other changes to fields are not currently supported at 10.1 and the remaining listed requests will be re-evaluated as separate ideas post 10.1 for inclusion in a future release. Hence, this idea will be modified to the 'Change field order' request.
How about allowing this via a GP Tool/Python. (Yes, I know of and much dislike 'field map') I bet most folks want to do it via script and not manually. Glad it's added to 10.1, have already used it.
This is the number one issue that users want fixed, ESRI this should be a top priority and be address this sooner than later. MapInfo (not that I’m a fan) has a "Modify Table Structure" that covers the ESRI user’s requests in this thread, obviously TAB files are different to GDB but there must be away to achieve this.
Please allow this functionality ESRI! We have replicas set up that must be unregistered and re-registered when we have to re-create a feature class or table because we want to add a new field in the middle of it.