Homebrew

You can now install Meld with Homebrew! On macOS, run:

$ brew install --cask meld

Other Homebrew Commands

I've changed the syntax of this answer over time to be more fluent. The following commands are equivalent and also work for at least macOS Sierra and High Sierra:

$ brew install --cask homebrew/cask/meld
$ brew install homebrew/cask/meld

You should not run the older $ brew install homebrew/gui/meld because it's deprecated by Homebrew.

As pointed out by @meduz in the comment above, meld now compiles file in brew (haven't tested yet), please try it first, since my original answer is much older.

Today is already possible install it using Homebrew:

brew install meld

I got a issue with pygtk, when I execute meld it says:

Couldn't bind the translation domain. Some translations won't work.
Cannot import: pygtk
No module named pygtk

I already have pygtk installed from lion, and needed to export it to work:

export PYTHONPATH=/usr/local/lib/python2.7/site-packages/

Add the above line to your ~/.profile to set PYTHONPATH automatically when you open a terminal window.

On OSX El Captain you have just to run:

$ brew install homebrew/gui/meld

When this question was asked, it was not possible using Homebrew. They didn't support it yet.

There are alternative solutions to installing meld on OS X:

Use a different package manager, like Fink, which is mentioned in meld's installation manual, or MacPorts, mentioned in the issue in Homebrew's issue tracker.

You can probably also compile from source, but need to get the dependencies yourself. Installing one of the other package managers might be easier than that.

I believe that the current correct brew commands are

brew install Caskroom/cask/xquartz
brew install homebrew/x11/meld

However after running those commands I ended with the following, which I know that I have overcome on other installations on different macs in the past.

Couldn't bind the translation domain. Some translations won't work.
'module' object has no attribute 'bindtextdomain'
/usr/local/lib/python2.7/site-packages/gtk-2.0/gtk/__init__.py:57: GtkWarning: could not open display
  warnings.warn(str(e), _gtk.Warning)
/usr/local/Cellar/meld/1.8.6/libexec/bin/meld:155: GtkWarning: gtk_icon_theme_get_for_screen: assertion 'GDK_IS_SCREEN (screen)' failed
  gtk.icon_theme_get_default().append_search_path(meld.paths.icon_dir())
Traceback (most recent call last):
  File "/usr/local/Cellar/meld/1.8.6/libexec/bin/meld", line 155, in <module>
    gtk.icon_theme_get_default().append_search_path(meld.paths.icon_dir())
AttributeError: 'NoneType' object has no attribute 'append_search_path'

But this time I decided it wasn't worth my time since I couldn't remember the exact remedy.

Instead I found a simple DMG installer and script from Alex Kras to launch the Meld application installed by the DMG installer. The instructions are on his site. Note, though, that this DMG-installed version doesn't respond well to to the git mergetool input