This is about writing characters you created either as part of an established universe like DC or Marvel or in your own universe.
In an established universe
1. No Mary Sues
While it is good to put some of yourself into an original character no one aside from you is interested in a fantasized version of yourself. Its more annoying than creative.
2. They need to fit in with the universe their in
I'm not saying you need to copy and paste some generic character to fit but they need to be easy to see as a character that would be interacting with these established characters. This is one of those tricky parts of writing because you have to balance what you're trying to do with what's previously been done.
3. Don't overpower your heroes
I know when you create your own character your first impulse is to make him the biggest badass in whatever particular universe your in but that doesn't fly if you want people to read and enjoy your stuff. If you throw out a character that debuts by knocking out Galactus its going to be hard to establish his problems dealing with lesser obstacles. Its Okay to make a ridiculously powerful villain because that makes it that much more interesting to see the heroes work out how to take them down. Just keep it within reason.
4. Make your character stand out
I know I said make your character fit in but you don't want them to just blend into the scenery either, again its all about balance here. There has to be something that makes them unique.
5. Don't be insulting unless your going for parody
Its fine to make a little fun of characters if that's your intention but if you're going for a serious story you should avoid being openly insulting to the established characters. I'm not referring to dialog here, it can be good to have an adversarial relationship between your character and an established one. What I'm talking about is taking the established characters and intentionally making them look bad in order to make your character look better. If you're trying to get people to pay attention to what you're writing you don't want them just getting pissed at you for making their favorite character look like an idiot (Unless they are intended to be in the first place.)
In your own universe
1. Again no Mary Sues
I can't stress this enough, its even more important not to do it in your own universe.
2. Don't make an infallible character
Nobody wants to read about a character that never makes mistakes, even Batman and Superman screw up sometimes. If you want your character to relate to people they need to be able to fail sometimes. I'm not saying they need to be an idiot just not perfect.
3. Your character needs to make sense in the world you've established
You need to set a tone in your world and if your character is the focal point they need to reflect that tone in some way. If you're trying to have a dark real world vibe you can't be having Rainbow Bright show up on a unicorn. Its very important that your character doesn't seem silly(Unless that's what you're going for.)
4. Make them relatable
Relatable doesn't have to mean realistic, it just means your character needs to have something in common with your readers. It could be physical limitations or a view point or even emotional hang ups. What's important is that someone can see a bit of themselves in them.
5. The most important rule
Don't take it personally if someone doesn't like your character, you can't please everyone.
This is just part 1 part 2 will be up tomorrow