As raylu says, zsh has that feature. Prezto (https://github.com/sorin-ionescu/prezto) makes it relatively easy to get started with zsh. Install it, enable any extra modules you want to load in .zpreztorc inside the “zstyle ':prezto:load' pmodule \” command, then update your .zshrc with your existing customizations from .bashrc and .bash_profile.

So like zsh? https://pastee.org/uka5q

Fish does that too: http://ridiculousfish.com/shell/

Now if someone could integrate that with bash-completions =)

And in case you're on a systems without such fancy shells as described in the other answers, the command "apropos [keywords]" will give a list of matching man pages.

Have you tried the bash-completion package? It adds a ton of context based tab completion stuff.