Add all files to a commit except a single file?

Question 1

I have a bunch of files in a changeset, but I want to specifically ignore a single modified file. Looks like this after git status:

# modified:   main/dontcheckmein.txt
# deleted:    main/plzcheckmein.c
# deleted:    main/plzcheckmein2.c
...

Is there a way I can do git add but just ignore the one text file I don't want to touch? Something like:

git add -u -except main/dontcheckmein.txt

Question 2

git add -u
git reset -- main/dontcheckmein.txt

Note: Git has subsequently added special syntax for this, which is explained in other answers.

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