This guide is dated to the pre-Apple Silicon / Big Sur era. For users on macOS 11.x Big Sur and above (Apple Silicon and Intel) see the new updated guide: Mac MAME Arcade emulation & NeoGeo using OpenEMU and SDLMame for Apple Silicon or Intel.
The last OS X native GUI is forever locked in 2013 at version .149.1 but fear not, you can run the current version of MAME ( version .180 as of writing this). However, there is a current MAME port for Intel OS X by @sdlmame_osx.
Download and install SLD
Go to libsld.org download and download the DMG. Then install the SDL2.framework into (in your root) Library/Frameworks. SLDL2 is a library for cross-platform development designed to provide low-level access to hardware such as I/O and graphics cards (many Steam games are based on this library for OS X).
Download MAME/MESS for Mac OS X - 64-bit Intel
Go to sdlmame.lngn.net and download MAME and decompress it into a folder of your choosing
Create Roms folder
Create a roms folder and place your roms within the newly created folder.
You can stop here but you'll probably want to download the m64 launcher from github.com/bamf2048/bamf2048.github.io (Direct link) to zip and place it in the directory. This will launch the app without the terminal and default to the installed games.
It isn't pretty but it'll get you the latest MAME compatibility. Notably sites like emuparadise have the rom sets. You may want to consider setting up OpenEmu with Mame if you want native GUI. Enjoy!