Short solutions that work with submodules, in hooks, and inside the .git directory
Here's the short answer that most will want:
r=$(git rev-parse --git-dir) && r=$(cd "$r" && pwd)/ && cd "${r%%/.git/*}"
This will work anywhere in a git working tree (including inside the .git directory), but assumes that repository directory(s) are called .git (which is the default). With submodules, this will go to the root of the outermost containing repository. 
If you want to get to the root of the current submodule use:
cd ''$(r=$(git rev-parse --show-toplevel) && [[ -n $r ]] && echo "$r" || (cd $(git rev-parse --git-dir)/.. && pwd) )
To easily execute a command in your submodule root, under [alias] in your .gitconfig, add:
sh = "!f() { root=$(pwd)/ && cd ${root%%/.git/*} && git rev-parse && exec \"$@\"; }; f"
This allows you to easily do things like git sh ag <string>
Robust solution that supports differently named or external .git or $GIT_DIR directories.
Note that $GIT_DIR may point somewhere external (and not be called .git), hence the need for further checking. 
Put this in your .bashrc: 
# Print the name of the git working tree's root directory
function git_root() {
  local root first_commit
  # git displays its own error if not in a repository
  root=$(git rev-parse --show-toplevel) || return
  if [[ -n $root ]]; then
    echo $root
    return
  elif [[ $(git rev-parse --is-inside-git-dir) = true ]]; then
    # We're inside the .git directory
    # Store the commit id of the first commit to compare later
    # It's possible that $GIT_DIR points somewhere not inside the repo
    first_commit=$(git rev-list --parents HEAD | tail -1) ||
      echo "$0: Can't get initial commit" 2>&1 && false && return
    root=$(git rev-parse --git-dir)/.. &&
      # subshell so we don't change the user's working directory
    ( cd "$root" &&
      if [[ $(git rev-list --parents HEAD | tail -1) = $first_commit ]]; then
        pwd
      else
        echo "$FUNCNAME: git directory is not inside its repository" 2>&1
        false
      fi
    )
  else
    echo "$FUNCNAME: Can't determine repository root" 2>&1
    false
  fi
}
# Change working directory to git repository root
function cd_git_root() {
  local root
  root=$(git_root) || return 1  # git_root will print any errors
  cd "$root"
}
Execute it by typing cd_git_root (after restarting your shell: exec bash)