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The one I want to use 95% of the time:

git diff-tree --no-commit-id --name-status -r <commit-ish>

From StackOverflow's How to list all the files in a commit? :

Preferred Way (because it's a plumbing command; meant to be programmatic):

$ git diff-tree --no-commit-id --name-only -r bd61ad98
index.html
javascript/application.js
javascript/ie6.js

Another Way (less preferred for scripts, because it's a porcelain command; meant to be user-facing)

$ git show --pretty="" --name-only bd61ad98    
index.html
javascript/application.js
javascript/ie6.js

• The --no-commit-id suppresses the commit ID output.
• The --pretty argument specifies an empty format string to avoid the cruft at the beginning.
• The --name-only argument shows only the file names that were affected.
• The --name-status argument shows the file names and how they were changed
• The -r argument is to recurse into sub-trees

If you want to get list of changed files: git diff-tree --no-commit-id --name-only -r <commit-ish>

If you want to get list of all files in a commit, you can use git ls-tree --name-only -r <commit-ish>

If you want to get a list of all new files in a commit, you can use: git diff-tree -r --name-only --no-commit-id --diff-filter=A <commit-ish>