Credit to Phil Meyer (a C4O cyclist) for this list - most of the comments are mine (Ben), but the outline was taken from his list.  I also listed some brand names - though just because you bought a different brand name, doesn't mean it isn't good.  However, I list the brand names in case you need a starting point.

Bicycle: ($500+) There are a few kinds of bikes that you can use: mountain bike, hybrid bike, touring bike, steel, aluminum etc. etc.  The $500 is a rough estimate.  A good indicator of a good bike, IMHO, is the nunber of waterbottle mounts.  If you see only one, the bike probably sucks.  2 is a minimum.

Winter is a great time to buy last year's model for getting a better deal.  Remember to haggle!  Usually shops won't budge on the price, but they WILL throw an accessory in to sweeten the deal.  Just pick any item below (as long as it is < $50 - you may have better luck than I do) so you don't have to buy it.  I convinced my salesperson to throw in a portable tire pump ($25).

If you buy a mountain bike: Get a pair of thinner, less aggressive tread tires.  1.5" are a good size.  If you feel more comfortable with wider tires (they are more stable) then fine, but you will feel a big speed difference if you use "slicks."

Bike Helmet - ($30+) Highly recommended.  If you don't like the look of a lunch bucket on your head, try the more expensive ones with the "cool" look.  Of course, the price goes up appreciably.  

Bike Light, Computer: ($20+) I got something that most people got, a CatEye Halogen.  I recommend it highly as you can remove it from your handlebar easily and use it as a flashlight (and also to annoy people by flashing the light on and off in their eyes...hehehe)

The computer is good for tracking distance travelled which is good to know if you're biking a really long way.

Bike Rack, Panniers, Fenders:  Go to Mountain Equipment Co-op (they're cheap there) for the fenders and get the Mt. Zefals that go around the tire.  There are cheaper ones that are around $25 - they do the job, but be warned.  It's ~$120 for the panniers (from MEC) and ~$15 for the rack (also at MEC).  Note that there is a front and rear rack available.  Get at least the rear rack.  Getting both front and rear improves weight distribution and will not affect handling as much.

Water Bottles, Cages:  A must.  A minimum of 2 large water bottles and a pair of the corresponding cages, as long as your bike can accomodate them of course.

Handlebar Bag - Probably around $50.  Other tourers suggest that it is highly recommended and can be the "administrative" centre of your tour - wallet, plane ticket, map, passport.

Bike Tools:  A must.  Don't think nothing bad will happen to your equipment, even if it's brand spanking new.  Here is a list (bring what you could use; if you do not know how to use something, no point in bringing it):

-spare tube(s) ($5)
-chain lube ($10) - don't use WD-40 - the oil is too light and will be gone in no time.
-portable tire pump ($25 - see the Bicycle section on how I got mine)
-chain rivet extractor ($10)
-spoke wrench and extra spokes($5)
-tire repair kit (to fix minor flats - the spare tube is for valve leaks or major tube damage) - get the glueless kind, it's less messy. ($5)
-an allen key set - get a foldable tool with 2-6mm allen keys(also known as hex wrenches) and it also has a Philips screwdriver head and a flat screwdriver head.
-that's all I can think of right now......

Tent, Sleeping Bag, Mattress, Stove:   It's about $160 for a two-person tent (though it realistically can only fit one) You're going to need these if you plan on camping.  Sleeping bags are rated in terms of temperature eg. rated to -5C etc.  There are also different kinds eg. mummy bags.

As for stoves, there are two different kinds: butane and white gas.  White gas is supposedly better in inclement weather, a little more pricey, and apparently more flammable.

Clothes: Well, this is self-explanatory unless you were planning on biking across Canada naked.  Cotton, while comfortable, is not good for physical activity.  It absorbs sweat and becomes very uncomfortable and you get that clammy feeling.  However, cotton is the cheapest.  Rain jackets are important if you want to ride in the rain -  there are PVC jackets that are completely rain-proof but are not breathable.  So you will sweat in them very easily.

The other, more pricey, alternative is gore-tex jackets.  They're around $350+.

Other Suggested "Small" Things: camera, diary(?), Swiss Army Knife(or just bring a knife, can opener etc), soap, shampoo, toothbrush, towel, toothpaste, sunscreen, swimming trunks, first aid kit, insect repellent, toilet paper

Other Tips:
- try night biking
- bring a book
- go to hostels if you get the chance - you'll meet lots of people
- make sure you got some way of buying things eg. credit card, bank card

Psychological Preparation

I don't know about this one, but I always believed you have to be mentally prepared for a trek like this.  If you have experience in touring for long durations, obviously you know what's involved, but personally, this is the first time (and hopefully not the last) I will be doing a long distance bike tour.

You have to be ready for bad weather, wildlife, bad traffic, bad riding-mates :), equipment breakdowns, and just plain bad luck.