As hihosilver stated, most times you are alright if you make fan art and want to share it on the internet. This is a gray area of legality, where basically making and sharing fan art is a privilege, not a right. Most developers allow for fan art so long as it's not distributed for sale or doesn't damage the product or developer's reputation. This is where you can research it and figure it out by looking at studio/publishers websites and their copyright/fanart policies.
For example, Epic Games has a policy regarding it that you can read. You can also assume that other developers would have a similar policy or standpoint except in specific areas.
http://www.epicgames.com/fanart.htmlNo one is going to go after you if you post a wip shot of Yoshi or Mario. Some developers even encourage and promote it so long as it doesn't damage their reputation. Others don't care to bother with the small fry even if their policy is against it.
Nintendo does have some policies you can read, though not specifically regarding fanart. It's more about distributing or using actual copyrighted material in your work, which is typically not legal whatsoever. You can assume most of their standpoint on the direct use of their media is about the same for other developers. Some links you can read:
http://www.nintendo.com/corp/legal.jsp#intellectualhttp://www.nintendo.com/corp/faq.jsp#graphicsDo remember that this applies to things such as taking a model of Link from a Zelda game and using it in a movie, render, or another game that you distribute, be it commercial or not.
You may be able to obtain permission to make fan-based movies/games for public release where all artwork is scratch-made and fan-based. I received permission to make a public Megaman Mod using the Unreal Tournament game engine a while back from Capcom. I've heard others have been denied such permission (for example, I believe the ChronoTrigger fan-game got scrapped because Square Enix sent them a cease and desist letter).
I hope this helps you understand a bit more about the legal aspect of using other people's work!