Stories are made of characters. It follows that if you want to write good stories, you need to have well-designed characters. Many times, the design of a character winds up being what sells a book, sometimes more so than the plot (Ian Fleming, I'm looking at you), and dynamic, well-thought out characters are usually the first thing people think of when reflecting on an author or a piece of fiction.
Last week I mentioned eight rules that Kurt Vonnegut wrote for fictioneers. One of my favorite of these is number three, which states:
"Every character should want something, even if it is only a glass of water."
While definitely not the kind of advice that can help you craft characters to steal hearts and sell books with, it is definitely something to keep in mind during character design. Most writers know to give their main characters goals and aspirations, but it is important to remember that every character, even those who fall in the 'everybody else' category, need to have goals and motivations and reasons to do whatever it is that they do. For your focal characters, you need to make sure that these motivations make sense and are consistent with their actions. A desire to bring honor to your family rarely involves kicking in doors and waving a sword, and greed doesn't make characters leap to block bullets. It's also important to realize that a character's goals affect more than just their general actions, it bleeds into their personality, their relationships, their appearance, everything.
One way I like to check the realism/believability value of my characters is to compare them to real people. Hopefully you aren't going to find your characters real-world counterpart, but you should still be able to draw parallels. "My friend George likes computers, went to school to be a programmer, but dropped out and plays video games instead," can have lots of parallels with, "My character, Eli, is a humble servant to the house of Wobblestein, but when faced with a hearty bribe, happily abandoned his allegiance and pocketed seven hundred pieces of silver." You can also try to draw parallels in history, theology, and even other literature. If you can't find anything remotely similar to your clinically depressed medieval soldier who decides that a path of revenge and womanizing is the way to solve his problems, that's not a hint that your character is original, it's usually a hint that he is not a well-designed character.
A lot of this may sound similar to Pat's "Economic Fiction" series of posts, mostly because it is. In order to avoid the Idiot Plot, characters need to have motivations that drive actions and make economic sense. Not everyone can get everything they want, so it is up to you, the author, to decide who will place what value upon what. Only after that decision is made can you begin to write something of any value or plot.