Here are three logos that I quickly did for fun in my free time, for one game I worked on and two of friends' games in development.
The Curse of Yucatan: A 3D exploration and puzzle adventure game set in a fantastic world. Some neutral, natural logo heavily inspired by Avatar's (just like the game itself), where I had the idea of turning the Y into a tree to really sell the primitive and nature of the game. This is the game that was our student project in third year of game art/design school.
Guild of Misfits: a story-driven strategy game where you manage an establishment, hire guilds of warriors and send them on quests around the country. The logo couldn't be more "royalty and medieval" than this. Maybe if I turned the underline into a sword? It would probably remind us of Kaamelott, if you have the reference ;)
Parazyte: A rail shooter inspired by Smash Hit, where you take your ship through the remains of cities destroyed by some strange entity that spreads like a parasite everywhere, where the game's fun factor comes from seeing what you shoot get destroyed with realistic physics. For it I made a sleek, modern but serious logo, reminding of lots of shooter games.
Some concept process was done in Krita but the vectorization/text editing was made in Inkscape.