I just wanted to list some of the tutorials I’ve found very helpful in familiarizing myself with the blender game engine.
Game Engine: Simple Character Part 1-3
These tutorials are so incredibly helpful to newer users, they cover everything from character animation to logic bricks to switching between scenes, you name it. A little lengthy, but both entertaining and extremely helpful. I would say a must for anyone new to the blender game engine.
Blender Tut 21: HUD, scoring and text
While this does take place in blender 2.49, everything shown in the tutorial still applies. Using scene overlay to make a HUD is a simple yet elegant solution.
How to create realtime-modifiable text within Blender 2.5
This tutorial covers purely adding and modifying real time text, but something nice that it covers is making your own fonts using FTBlender. If you have a word processor, you can actually find the font files in those folders and use those to create your own fonts in blender.
Real Time Shadows: Blender 3D Game Engine 2.5
A simple, step by step tutorial of what you need to do to get real time shadows in the blender game engine. This site has some other good tutorials so you might want to take a look around.
Anything by SolarLune
This guy is a wizard over on BA’s Game Engine forums. Any time I’m searching for a thread that already answers my question, it seems like 75% of the time he’s the one providing the answers. This link is specifically to the BGE Tutorial section, look to the panels on the right side of his webpage for links to even more information.
Anything by Ira Krakow
This guy has made a good number of blender tutorials, many of which cover Python in blender, or the game engine. I would say especially good for people new to programming or Python that would like a push in the right direction.
Hopefully these help! I found these incredibly useful and wish I had them when I started learning, so hopefully these end up helping someone else. Enjoy!