I'm experiencing a similar error to slsharma; I've found that the issue was resolved when I quit and re-started ArcMap. I never experienced this problem at all using 9.3 and though I should perhaps do my field calculations in an edit session, this process has been a no-brainer until recently.
Should this issue be reported as a bug or at least have more attention directed at it? This could lead to some catastrophic loss of data for someone who isn't being careful.
Joe Champagne has one solution; I can't get even this to work, when trying to calculate selected records in a feature class produced as a result of several geoprocessing steps (Clips, Dissolve, Unions). I never had this problem with the same type of files in ArcGIS 9. I'm now working with ArcGIS 10, SP3. I am using the unsatisfactory solution of making a new copy of my file each time, and then the selection rules are observed. Sometimes an export also works. It's an annoyance, and as Joe suggests, it should be viewed by ESRI as a bug of some sort in ArcGIS 10
If you are at 10 sp3 and performing the field calculation on a layer that participates in a join there is a bug where the field calculate will process all the rows instead of the selected row, NIM076496.
In my experience with using the Field Calculator, I have observed the following:
i. When calculating all records in a field, simply make sure no record is selected/highlighted.
ii. If the calculation is to be applied to only selected records, then, it becomes necessary to commit any unsaved edits before proceeding with the calculation. For some weird reason, if edits have not been saved, the Field Calculator does not handle edits pending in the cache properly. However, once Edits are saved, the calculation is automatically applied to only the Selected records.