How to get just one file from another branch

git checkout master               # first get back to master
git checkout experiment -- app.js # then copy the version of app.js 
                                  # from branch "experiment"

See also git how to undo changes of one file?

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Update August 2019, Git 2.23

With the new git switch and git restore commands, that would be:

git switch master
git restore --source experiment -- app.js

By default, only the working tree is restored.
If you want to update the index as well (meaning restore the file content, and add it to the index in one command):

git restore --source experiment --staged --worktree -- app.js
# shorter:
git restore -s experiment -SW -- app.js

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As Jakub Narębski mentions in the comments:

git show experiment:path/to/app.js > path/to/app.js

works too, except that, as detailed in the SO question "How to retrieve a single file from specific revision in Git?", you need to use the full path from the root directory of the repo.
Hence the path/to/app.js used by Jakub in his example.

As Frosty mentions in the comment:

you will only get the most recent state of app.js

But, for git checkout or git show, you can actually reference any revision you want, as illustrated in the SO question "git checkout revision of a file in git gui":

$ git show $REVISION:$FILENAME
$ git checkout $REVISION -- $FILENAME

would be the same is $FILENAME is a full path of a versioned file.

$REVISION can be as shown in git rev-parse:

experiment@{yesterday}:app.js # app.js as it was yesterday 
experiment^:app.js            # app.js on the first commit parent
experiment@{2}:app.js         # app.js two commits ago

and so on.

schmijos adds in the comments:

you also can do this from a stash:

git checkout stash -- app.js

This is very useful if you're working on two branches and don't want to commit.

git checkout branch_name file_name

Example:

git checkout master App.java

This will not work if your branch name has a period in it.

git checkout "fix.june" alive.html
error: pathspec 'fix.june' did not match any file(s) known to git.

Everything is much simpler, use git checkout for that.

Suppose you're on master branch, to get app.js from new-feature branch do:

git checkout new-feature path/to/app.js

// note that there is no leading slash in the path!

This will bring you the contents of the desired file. You can, as always, use part of sha1 instead of new-feature branch name to get the file as it was in that particular commit.

Note:new-feature needs to be a local branch, not a remote one.