cd to a directory by typing its name?
autocd was added in bash 4.0. You can install a newer version of bash with Homebrew and then change the default login shell with chsh:

brew install bash;echo /usr/local/bin/bash|sudo tee -a /etc/shells;chsh -s /usr/local/bin/bash


After you open a new login shell (or a tab by default in Terminal or iTerm 2), echo $BASH_VERSION should print something like 4.2.45(2)-release.

Terminal and iTerm 2 open new shells as login shells by default, so bash reads ~/.bash_profile but not ~/.bashrc. If you don't source ~/.bashrc from ~/.bash_profile or anything, add shopt -s autocd to ~/.bash_profile instead of ~/.bashrc.