Thanks to all for the input.
A little more info--there are two songs I've been working on recently, "Hey There" and "Chattanooga Choo Choo." I have sheet music for both, and it seems to me that the chord sequences are essentially correct. (They are rather "busy" sequences, and "Choo Choo" in particular has a number of chords that I've simplified or dispensed with, but the portions with the diminished chords strike me as right on.)
One of these songs has a passage that goes F-F#dim-C, the other one has a passage that goes F-Cdim-C. It just struck me as odd to use the "F#" nomenclature in the key of C, which virtually never has F# chords, especially when the "C" nomenclature is available to name what is for all intents and purposes (as far as I know) the same chord.
On a side note, related to M. Ted's observation above on 7th chords, I've noticed that this Cdim chord can sometimes substitute for, or be substituted by, a D7 or B7. In either case, 3 of the 4 notes are the same, and in certain situations the one chord sounds about as right as the other. A handy little trick to have up one's sleeve.