The right way to solve this is to enter:

$ cd "$(brew --repo)" && git fetch && git reset --hard origin/master && brew update

Found at http://discourse.brew.sh/t/how-to-upgrade-brew-stuck-on-0-9-9/33.

Just prefix your install command with HOMEBREW_NO_AUTO_UPDATE=1, like this:

HOMEBREW_NO_AUTO_UPDATE=1 brew install somepackage

Source: brew manpage

This was easily done with scripts and now the built-in autoupdate mechanism handles this elegantly. See Tate’s excellent answer for details

If the automatic update and upgrade aren’t working, here is another way for older versions.

For efficiency (and cool factor), I would use a tool like Lingon to launch this script periodically using launchctl/launchd instead of each time you start a shell. On my MacBook, it takes 3 seconds to update the second time (no work done, DNS cache set, etc...) and it take 10 second to run the first time (no work done) or 15+ seconds if a package needs to be downloaded or compiled.

Perhaps once a day or once an hour - running in the background would be sufficient given those times to execute?

You could make a simple script /usr/local/bin/brewup that calls brew in turn and logs the results to the system log. If you don’t like chasing logs in the centralized log store, “teeing” them to a text file works well, too.

#!/bin/bash

brew=/usr/local/bin/brew
logger=/usr/bin/logger

$brew update 2>&1  | $logger -t brewup.update
$brew upgrade 2>&1 | $logger -t brewup.upgrade
$brew cleanup 2>&1 | $logger -t brewup.cleanup

I just call the brewup when I'm about to go make tea or when I get started and let it run in the background.

brewup &

Per homebrew code on github, this shows all apps that can be updated:

brew outdated

brew help does not list the command, but it is documented in man brew.