Regarding pictures based on other existing works or characters, this falls to the copyright conditions that the person whose intellectual property it is has imposed. It's important that you're fully aware of them before you do anything that just might result in "BAWWW YOU STOLED MY STUFF I SUE j00 NAO D:<"
In general: Images that has that c in a circle sign (the old copyright) on it- no direct reproduction or alterations to that work without express, written (documented) permission from the person cited in the copyright. You may usually do work 'based' on it i.e. a specific element or composition technique, but in these cases it's always best to cite: "based on such and such".
Concepts, characters and ideas that have a c on it, like Disney characters etc., it varies. Fanart generally won't get you into trouble unless one of Disney's thousand and one lawyers (probably much more than that, to be honest) finds your image and HQ decides it's not appropriate to associate the image with Disney, at which case the lawyers will stand around you with e-cudgels and tell you to take the image down before they pwn your sorry butt with MULTIMILLIONDOLLAR LAWSUIT ATTACK. Generally they can't go around doing this to everybody so there's a line to be drawn, and the lines drawn on this forum about what you can and cannot post (no obscene material) are far more restrictive.
So for copyrighted characters and stuff that's intellectual property, just say 'this is based on so and so and this character is copyright Disney' or whatever it happens to be. Beware: some organisations will additionally add the clause that while you may draw fanart you are not allowed to appropriate the concept in any way i.e. adopt the character for roleplay or even as some representation of you. Many people don't realise this because a lot of the time, knowing this requires reading the bloody fine print.
Other people (amateur artists) who are really insecure about their work say 'NO TOUCHY'...it's just best to leave those alone ^^;
More recently new forms of distribution license that actually have some credence have come up, notably the 'copyleft' licenses (represented by a backward copyright sign, lol) such as the GNU Free Documentation License, which basically say "you can do what you like to this so long as you don't touch the licensing conditions." Creative commons is a notable example of this that allows people to grant certain rights to the public regarding their work, like whether you can change, distribute etc.
This can be confusing and it's certainly not perfect but you should expect to run into more of these in the future as they grow and change! For most amateur applications, the simple rules "credit given where credit is due" and "better to seek permission than ask forgiveness" apply.
