(Just gotta comment on this part first...)
Do not slice with your blade. A slicing motion will not disable your opponent. Only stabbing in a vital organ below the ribs is effective. The ribcage can catch your blade, so aiming for the heart is harder than it may seem.
... At least that's what I was taught in Combat TKD!:enguard:
Not sure if this part was what you were taught in Combat TKD (or the advice on commiting seppuku to avoid the Terminators, ha!), but I'd actually disagree with this advice. To take it piece by piece....
Slicing can be very effective, provided you choose your targets well. A lot of my knife stuff comes from Michael Janich and his MBC (Martial Blade Concepts), and slicing is taught as very effective there. In fact, I teach a number of programs for knife which are almost exclusively slicing actions, or combination thrust/slice actions. The primary concepts there are to slice to the limbs to disable them (disarm by slicing into the arm, stop the opponent from following by thrusting/slicing into the leg), and these programs are non-lethal responces to armed attacks. Slicing attacks to the body, I agree, are mostly ineffective, but a good cut across the tendons in the forearm will remove the use of that arm pretty much immediately. And a slice to the throat, well, Japanese blade work is predicated on slicing over thrusting, and has been for centuries now, so I'm going to feel it has some merit to it.
When it comes to stabbing a vital organ below the rib cage, that can take a lot longer than most think to actually have the desired stopping effect (whereas the slicing cuts to the limbs, disabling and disarming, can end a fight in a fraction of a second), as it can take hours to die from a belly wound. This is why in seppuku you have a second to decapitate you; simply plunging a blade into your belly isn't enough. In a best-case scenario, it generally takes up to 5 or 10 seconds for someone to bleed out enough to lose consciousness, and another 10 to 20 seconds for lethality to occur. And that's if you got an artery or vein, not an organ. Douglas Fairbairn did many great things for understanding close combat, but things like his generally accepted "Timetable of Death" (how long it takes to die from various injuries/wounds) are largely guesswork with little actual evidence to back them up. In fact, a number of his claims go against medical knowledge. Michael Janich became aware of this (I believe) through his training partner and Colorado Police Officer Christopher Grosz' investigation of the Timetable, and began formulating his approach to bladed combat with the new, more accurate information in mind. For anyone interested, I cannot recommend this book enough:
http://www.budovideos.com/shop/customer/product.php?productid=23916
When thrusting to the chest, yes the ribs will get in the way, but if you turn the blade sideways you will increase your chance of it deflecting off the ribs and continuing to penetrate. You may very easily chip the tip of your knife, but I can live with that. Thrusting to the heart, however, is still less likely. It is a little deeper than you would likely thrust, and is protected by muscles and sacs around it. More likely (and just as deadly) is that you will instead penetrate the lungs, essentially ending with the other guy drowning in their own blood as it fills their lungs.... all the kiddies gone to bed now? Good....
As said, though, my focus in knife combat is non-lethal, and based on fight-stopping, as many lethal actions don't stop the other guy long enough for you to actually be safe. But fight-stopping actions do. And I'd rather bet on that as an aim, rather than just killing someone (not something I'd like to do, actually).
Now, on to my "basics" of knife fighting.....
If they have a knife, odds are you won't see it. If you see it, odds are they don't want to use it, and are just trying to scare you. If this is the case, go along with it, and don't engage unless there is a real threat.
If you get stabbed and don't see the knife, odds are (due to adrenaline and other aspects) you won't feel it. It'll simply feel like a punch. Until you feel weak and fall over, that is. If you end up rolling around with someone and get hit in the body a bit (or even if you don't know if you were), when you get up, pat yourself down and feel for warmth and wetness. These are not good signs.
Some of the most common stabbings occur at the hands of the friend/girlfriend of the guy you're fighting.
A thrust only needs to be about an inch deep to be lethal.
If you manage to get at least 21 feet from a knifeman, you are only starting to get close to a safe distance to escape.
In a knife fight, generally only one person has a knife.... and generally the other doesn't know it's a knife fight.
If you are using a knife (defence against another weapon attack, knife, club, baseball bat, etc), keep the knife in front, and don't extend unless you want to offer a very deliberate target.... it will be hit/cut at.
Be aware of the natural responces of a knifeman in your training. They don't like it when you try to take their weapon.
Control of the weapon is everything. Once you have it, get it into a safe place and keep it there.
Being cut on the way to gaining control is acceptable, getting killed is not.
Knives can be hidden incredibly easily, be aware when you can't see someones hands... especially if they're showing any pre-fight indicators.
(Okay, a fun one...) Knives are dangerous.... but nowhere near as dangerous as the man holding the punnet of strawberries! Release the tiger!