I think we're getting to a point that you are addressing both "stance" and "footwork." While being two seperate things, they are related. However, I'll just chime in with my two cents on footwork.
Mark Hatmaker states that footwork is integral to a fighter. In his words he described punches and kicks as being a martial artists weapons, or destructive payloads/warheads in our arsenal. Footwork (the ability to move around, cover distance and whatnot) is the vehicles of transportation used to bring those weapons into their destructive range. Likewise the same means will be used to move you away from your opponent's line of fire and out of harms way.
Bruce Lee was also a huge proponent of developing effective footwork. He was very high on Ali's footwork, and dedicates a great deal of the opening text of the Tao of Jeet Kune Do on footwork alone. I like how Kin put it, footwork is what makes fighters different from heavy bags. No one fights each other standing still if they have a choice about it.
I won't go into the subtleties of Ali's footwork, but I can give you an idea or two how to develope better footwork.
1) Dance. It doesn't have to be anything specific, you can choose between b-boying, ballroom dancing, line dancing, crunking, or any combination thereof. Unlike tight-rope walking, using jump/platform shoes, single-leg squats or overhead squats, dancing will teach you how to maintain a dynamic center of balance, coordination, and will give you a hell of a cardio workout. Rhythm and timing is also engrained into the person in a constantly moving environment. Is it a random co-incidence that many traditional styles of martial arts were trained in the form of dance? You think it's a co-incidence that the most technically sound striker in the UFC (Anderson Silva) also knows how to dance
2) Shadowboxing. You should do this in two stages. In the first stage, you do simply do shadowboxing rounds without punches. In this you would simply move around utilizing footwork to traverse the ring area and "throwing" punches without the arm extension, while practicing your covers, dipping, leaning, and other defensive movements. Most people shadowbox wrong in the sense that they are too static and they tend to admire themselves too much in the mirror. This is to train your core movements, and get your base (your feet) under you first. Do this for a few rounds then move to the next stage.
The second stage is full blown shadow boxing with the arm (or leg) extension included. By this time, the ballistic feel of utilizing your core and legs for attacking should be finding a home in your muscle memory. Adding the limb extension to the movements will really begin to test your balance, but will simply add on to your base. Remember, you must move while shadowboxing. You have to have a mental opponent in front of you and you move in tandem to that opponent.
3) Jab and move drills. The jab is a weapon that is best used by a moving practitionet. Ali, Robinson, Leonard, and Hearns all knew this and used the jab as their primary weapon in the ring. A lot of footwork drilling can be done with the jab. The key to this is to be light on your feet, and ready to move in a way that allow your base to stay under you. That way your balance isn't compromised, and you can still attack.
Here's a few starter drills:
From there add multiple jabs:
Mixing it up more could look like:
Jab>Step In>Jab>Step Out
Jab>Circle Left>Jab>Step out
Then switch levels of those jabs between head and body:
Jab Head>Jab Body>Step Out
Jab Body>Step Out>Jab Head
Jab Head>Circle>Jab Body>Step Out
Jab Body>Jab Head>Circle
You can even include sprawls and shots:
Jab Head>Circle>Jab Head>Shoot
Jab Body>Step Out>Jab Head>Sprawl
There are other basic drills you can find with a little research. All go a long way in helping with footwork. Bad foot work will get you killed in a fight against someone who is trained. I remember the Final to the Ultimate Ultimate UFC in 96 where Don Frye fought Tank Abbott. Well, for the first minute of the fight Tank is just blasting Frye with a bunch of punches (Don's face looked like hamburger at the end of the fight) and was sure to win until he tripped over his own two feet while Don pressured him. After Tank went down, Don climbed his back and sunk in a Rear Naked Choke and solicited the tap at one minute and 22 seconds into the first round. I've heard a few of my friends say that the end of the fight was bullshit, and that "If it was a real fight out in the streets, Tank would have killed Don." My only reply to that was, "If it was a real fight, Don wouldn't let go of the choke until Tank was unconscious. He could do anything to him he wanted to after that."
All because Tank tripped over his own foot.
I'll leave you with some vids to contemplate:
The "Drunkin' Master" Emmanuel Augustus
Willie "Will O' the Wisp" Pep vs Armand Savoie
Notice the footwork off the jab?