Technically - you do not need to purchase anymore games. However, you will need to purchase and download (possibly) Counter Strike: Source and Team Fortress 2 for a lot of the textures and other game objects.
From the Steam page for Garry's Mod:
Please note: Some multiplayer servers and game-modes might require you to own other games - such as Counter-Strike: Source and Team Fortress 2.
This Reddit also provides some more details.
Counter Strike: Source is currently $19.99 at posting. Team Fortress 2 has been free since June 23, 2011. It's important to note that some others games that may be needed are basically any game that run on the Source Engine developed by Valve. This includes some games like:
- Left 4 Dead
- Left 4 Dead 2
- The Half Life 2 Series
- Counter Strike: Global Offensive
...and many more! But, the majority of the textures are handled with just Counter Strike: Source. I would say at the minimum, you will need that game (and you might as well get Team Fortress 2 since itsit's free). A complete list of sourceSource games can be found here.
By not having the correct games, you could potentially be missing the textures needed to play maps created by others. You will see a lot of checkered purple and black objects, and actual "ERROR" messages like this: