Overall Description Edit
User Interface (UI) is a really important aspect of a game because User Interface can show players the information they need to play the game, and usually User Interface is the most straightforward way to show players the core mechanics of a game. However, different players have different preferences about User Interface, therefore being able to customize it freely is a really nice feature to the design of the game as players can customize User Interface in a way that they are most comfortable with.
Example for Demonstration Edit
Most games that have this feature are MMORPGs, but other games can totally use this feature to give players freedom. I'll take TERA as an example.
TERA is an MMORPG developed by Bluehole Studio in 2011. In this game, the User Interface contains (1) a health bar and a mana bar with stamina indicator, (2) a channel indicator and a location indicator, (3) a compass, (4) a minimap, (5) a chat box, (6) a skill and item bar, (7) a menu bar and (8) a quest log window. Players will be able to move as well as scale all of those UI elements freely on screen. This design feature allows different players to customize their UI to their preferable style.
To visually experience how this feature is like in TERA, please watch this video.
World of Warcraft
As mentioned earlier, many MMORPG's allow the player the ability to customize their UI. While the native game gives you some options, World of Warcraft allows you to download and install various addons that can greatly change how the game's UI looks and functions. These addons allow you to slightly alter how you physically play the game and experience the game's raw data (health, mana, XP, etc.). Whereas the game and the experience you get from playing it doesn't change much from tweaking the UI, it allows the player much more authority over how they want to deal with absorbing this raw data.
Banished is a real time strategy/resource management game where the player controls a group of settlers 'banished' from their former home with the goal being to grow the population and build a bustling city. Given the nature of the game, managing the settlers' jobs and the stockpiled resources is of paramount importance to succeeding in the game. This is facilitated in part by the flexible UI the game offers. The player has a myriad of windows they can drag onto the main game screen ranging from a map of the area to a list of current resources to an assignment page for settler jobs. The quick reference and control afforded by having these windows on the screen can aid the player in the quick decisions sometimes called for during gameplay. The player is free to pull out as many or as few as they would like and arrange them on the game screen however they find it to be most beneficial.
LotRO (Lord of the Rings Online)
This game allows the player to move and resize UI itens to whatever please them on the screen, so the UI would not be placed in an annoying point of screen. I feel like instead of studying the best solution for the UI elements placement they created a new solution by giving the player the "job" of trying it out and find the placement themselves and it worked!