Since -i keeps STDIN open even if not attached, it allows for composition (piping).
For example:

docker run --rm ubuntu printf "line1\nline2\n" | docker run --rm -i ubuntu grep line2 | docker run --rm -i ubuntu sed 's/line2/line3/g'

^{(Source: issue 14221)}

Or:

$ echo hello | docker run --rm -i busybox cat
  hello

^{(Source: issue 12401)}

Now imagine this not in front of a keyboard and being used in a script where you can actually write to the processes stdin through something better than a shell |: example integration-cli/docker_cli_attach_test.go

As noted in the comments by Pixelbog, adding the --rm option avoid leaving a bunch of ‘Exited‘ containers.