There are three simple techniques to create a nice sky in a game.

• Skybox: Good when the sky can be viewed from all directions. For example in a space game. It is basically a box with inverted faces.
• Skydome: Probably the best choice when rendering outdoor scenes with terrain. For example a driving game. It is basically a half sphere (dome) with inverted faces.
• Skyplane: Sometimes an option when rendering outdoor scenes and you should not be able to see the horizon. It is just a plane with the normal pointed down and a sky texture attached to it.

Information and tutorials about skyboxes:
http://www.toymaker.info/Games/html/skybox.html
http://www.gamasutra.com/features/19981023/bell_01.htm

Information and tutorials about skydomes:
http://www.spheregames.com/index.php?p=templates/pages/tutorials
http://www.riemers.net/eng/Tutorials/XNA/Csharp/Series4/Skydome.php
http://www.flipcode.com/archives/Sky_Domes.shtml

A method that approximates the vegetation, in this case the trees, with billboards when viewed from far away. This seems to work like a more advanced impostor as it uses more than one billboard per tree/object. The image below shows to the right how the tree is split up into multiple billboards.

Link where you could find the paper:
http://graphics.uni-konstanz.de/publikationen/2005/hybrid_level_of_detail_approaches/Colditz%20et%20al.%20–%20Real-Time%20Rendering%20of%20Complex%20Photorealistic%20Landscapes%20Using%20Hybrid%20Level-of-Detail%20Approaches.pdf

This algorithm for rendering grass allows user interaction with the grass which most other methods won’t. They call this interaction effect treading and it’s implemented as a scalar field which determines in which direction the individual grass straws should bend.

Link to the paper, more screenshots and movies
http://www-evasion.inrialpes.fr/Publications/2003/GPRFC03/

Nearly the same as a Octree but instead of dividing the space in cuboids in 3D it’s rectangles in 2D space. This is useful for rendering terrain and you want to cull a lot of the terrain fast.

A visual demonstration of a quadtree used for fast collision detection:
http://lab.polygonal.de/2007/09/09/quadtree-demonstration/

Introduction to quadtrees and sample code:
http://www.gamedev.net/reference/programming/features/quadtrees/

More info about quadtrees, including source:
http://www.kyleschouviller.com/wsuxna/quadtree-source-included/