I have a big MP3 library, all of it carefully tagged with the Tag and
Rename program; as far as I know, the ID3v1 and v2 versions of the
tags are the same, save for the former being shorter. But when I
import my songs into iTunes, or transfer them onto my iPod, I see
entirely new tags. For example, a recording of "Parsifal" I ripped
myself has "Wagner" for the artist in all the MP3 fields. But in
iTunes, it's "Wagner" in some of the files, but "Wagner - Karajan" in
others --those corresponding to disk 2 of the 4-disk set. Where is
iTunes getting these tags from? I can't see them anywhere. And how do
set all the iTunes tags to the way I have them for my MP3s?

I had the same thing happen to me. It turned out that the
Orchestra/Band field was set. Double-click on the song in Tag&Rename,
click on Additional and see if any fields are set there.

You can use Tag&Rename to fix it. Use Tools/Copy text from one tag
field to another. Select Artist as the source and Band/Orchestra as
the destination.

That seems to do the trick; many thanks! Actually, it looks like
iTunes first looks for the "Album artist" field, and if that it blank,
it uses "Artist." My problem was that I didn't know the Album artist
field even existed; it is not in the main batch of tags on the first
screen of Tag and Rename. You need to go to "Edit all supported tags"
to see it. I checked all my files, made the Album artist field blank,
checked the field, and the saved the tags out. This overwrote whatever
info may have been stored there from CDDB, etc. If you do this, be
sure all the other fields aren't checked when you save the tags, or
else your good info will be zapped.