Let's assume that you can start a fire under good conditions.  For instance, if you've got paper, matches, and axe, dry wood, and you're on good solid footing in reasonable weather.  Does that mean you're ready to adventure in the woods?  Venture out on a snowmobile in the winter? Fly in a bush plane over some remote and rugged terrain?  Float a canoe down a quiet October river hunting some moose?  What happens if you get the sled stuck, or the plane is forced down, or you tip the canoe into water that is barely above the freezing point?  What if it starts to snow?  In a situation like that being able to build a fire will be the difference between living and dying.  

If you've grown up in the country or in the bush you'll have no problem.  You'll just throw some fuel together and get 'er going.  But if you're that guy you probably aren't reading this article because when you saw the title you'd have said "Yeah, whatever".  Its pretty safe to assume that if you're readig this you're not certain that you could start a fire under those conditions. Here's how you can improve your odds, and in doing so improve your chances of surviving.

First, assume that you're going to get into a jackpot and that you'll need to start a fire.  Make sure you have waterproof matches and a way to light them.  Get big fat ones that don't break easy.  Failing that, have a lighter that is easy to light. Don't get a fancy one or a child proof one.  If you need to start a fire in adverse circumstances there's a good chance that you'll be very cold, and possibly very wet, and your hands won't be working really well.  Make it easy on yourself.  

Some people dip the heads of wooden matches in wax.  That way they stay dry but the wax will scrape off. If you use this method use strke anywhere matches.  If you need the striker board, and its wet, it won't matter if the match heads are dry.  Its possible to keep the striker board dry inside a container, but cold wet hands can knock it out of commission.  

Second, bring some good fire starter that you've used before.  Those little white cubes of barbeque starter might work, but make sure.  Sometimes they burn very poorly.  Don't depend on something you haven't tried.  An option that my Dad swore by was something he called "quickstart" - a mixture of gas and motor oil.  It burned slower than straight gas, and lit quicker than diesel.  We used to put it in a glass jam jar and wrap it up in a pack, and then were careful not to break it.  The advantage was that if you dumped a canoe but retreived the pack you could smash the bottle no matter how much you were shaking with cold, and any match you were able to strike would ignite the mixture.  Nowadays you could put it into a sealable plastic container and if you were too cold to unscrew the top you could just stomp on it to get the fuel out.  Whatever you take remember two things: its not cheating if you use an accelerant to build a fire in a survival situation, and make sure that your accelerant will catch easily and burn slowly.

Carry a sharp, sturdy fixed blade knife that can cut sizeable pieces of wood, or bring a small hatchet.  Keep it sharp.  Sharp tools are safer and more useful than dull ones, which end up cutting you more than wood. 

Keep everything together in a small backpack that is easy to carry and that you can keep secure but close to you.  If its not comfortable you won't take it.  If its not close to you and secure you'll lose it if the boat tips or the plane sinks.  If you've ever looked at your ride home sink or float away without you you'll know how nice it feels to have a survival pack with you, and not with your ride.

Remember that we prepare for emergencies becasue we don't know when they'll happen but we do know that they'll be dangerous.  Whenever I think of starting a fire in bad conditions I think of a time many years ago when my brother and I were moose hunting. He dropped me off on the river bank so I could walk the ridge and maybe scare up a moose.  He drifted quietly downriver.  He made better time than me, as we knew he would, and stopped after a mile or so to do some fishing. While playing a nice Rainbow his collar got hooked on a tree branch and he was pulled out of the canoe.  The water wasn't deep, but he was soaked to the skin in near freezing temperature.  Luckily he grabbed the bag, broke the bottle of quickstart and got a fire going, but it was a near thing - he was shaking so badly he was almost unable to hold the matches.  I came upon him right after he got out of the water, but I was on the other side of the river.  If he hadn't had the makings for the fire I don't know what I would have done, but I do know it would have been scary.  Shit happens in wild country.  If you want to survive it try to be prepared.