Below is listed some of the kit you may want to have in your canoe. The items near the top of the list are the ones you are likely to need sooner than the ones at the bottom.
PFD or lifejacket (see THIS forum thread)
PFD (personal floatation device), Buoyancy Aid or Life Jacket is an essential. It is no accident that I have listed this before even a paddle. Going out in a canoe without some sort of personal floatation is asking for trouble. The choice of the style is wide and will be largely down to the type of water you are out on as well as the season. From the above thread on the forum you will see that there are a number of views on the various options but the one thing that is agreed by all is that you should be wearing one of some sort or another.
Goes without saying that you will need a paddle. The choice of paddle is almost as difficult as the choice of canoe. Plastic or wooden. Beavertail, Ottertail, bent shaft etc. As with the canoe the secret is to try as many styles as possible and go for the one that suits you best. Be warned, it may not be the one you like the look of best. My favourite paddle to look at is a lovely wooden Beavertail one but I find a gaudy plastic and aluminium paddle the best to use.
Without a spare paddle eventually you WILL be up the creek without a paddle. Paddling a canoe with your hands can be hard work. Some people even carry a take apart double bladed paddle for use as a spare and in heavy weather.
An essential piece of safety equipment. Have it with you always. The sound of a good whistle will carry far further than the loudest of shouts.
First Aid Kit
If you don't know why you should have one of these then you really should not be going out anywhere. A first aid kit should be checked and restocked regularly. The size of the kit should reflect the length of the journey. A few hours out on the canoe may only require a few plasters, pain killers and bandages but a more comprehensive kit would be required for a multi day trip.
Bail & Sponge
You will get some water in your canoe. Hopefully it will just be a small amount which you can take care of with the sponge, however, likely as not you are going to one day need to bail out a larger amount. If you do not have a bail with you getting a fair amount of water out of the canoe can be quite difficult. Trying to use the canoe when it is half full of water is pretty difficult and in heavy weather damn near impossible.
Rope / Cord
At the very least you will want enough cordage to tie your stuff to the canoe so that if you suffer a capsize it does not all drift away. Dog leads from the £1 shop are handy for this. You will also want some rope at the ends of your canoe to tie it up if you land at a jetty.
Knifes have suffered a bad press lately but it is essential that you have a knife with you in an open canoe. With cord and rope about it is essential that you have the means to cut yourself free if you become entangled. The knife must be easily accessible. A fixed blade is strongly recommended over a folding one. Serrated blades will handle rope better that smooth. There are a number of knifes designed as rescue knifes that have serrated blades and a blunted point.
Obvious really. From keeping your lunch dry to your phone and car keys. These come in every size you could need and are reasonably priced. You can also get ridged boxes that will keep kit dry, most notable are Peli cases but in my experience these offer few advantages over the traditional dry bag. Where they may be worth the extra money is for expensive cameras etc.
For a short trip back in the car or more usually in the Dry Bag. You know it makes sense.
This is a length of rope in a bag, which as the name suggests you can throw. It can be thrown to another canoe needing rescue, streaming the rope behind it. Or it can be thrown to help on the land. If you suffer a capsize you can also grab it and swim for shore, hopefully reaching shore before the rope runs out. Thus enabling you to pull the canoe ashore rather than having to swim it ashore.
Air Bags / Buoyancy
These large air filled bags can be tied into the front, rear and middle of the canoe. These keep the canoe afloat and high in the water even if swamped. A similar effect can be obtained by having all your stuff in dry bags securely lashed in to the canoe.
There is no shade on the water so a wide brimmed hat is an essential in the summer and handy for keeping the rain of in the winter. You do not have to buy a Tilley Hat but you will eventually A warm wool hat is also a good idea as when it is cold there is no shelter from the wind. A wool hat will retain a lot of its insulation even when wet.
Any sunglasses will be handy but polarised ones will really cut down the glare from the water.
I have not specified what type of footware as there are various opinions on this and it will depend on the season but essentially your foot is going to go into the water at some point and you need to be prepared for that. Also you want it to be something that will not hamper you too much if you have to swim. The subject of footware was discussed in THIS thread on the forum. I will let you make your own choices.
A soft mat to kneel on when you are paddling. Of course you may choose to sit but kneeling generally gives you more control. Without a mat your knees will suffer.
Food and Water
Always a good idea to have some food to top up your energy levels and water to stop you getting dehydrated. I know you will be paddling on water but it is rare for it to be drinkable without any treatment.
You do not always paddle. A pole can be used for making progress against the current and in shallow water in heavy weather. They are also useful when lashing canoes together or for pitching a tarp.
Usually used for storing kit. fairly waterproof but best to have a dry bag inside. Will protect gear from bashing etc.
Yes you do not need to paddle all the time. There are a range of sails available for open canoes. From the simple to the sophisticated.
Trolly / Wheels
For transporting your laden canoe over relatively short distances. Could be from your car to the put in point or between one part of your paddle across a short piece of land to another put in point.
Drogue / Sea Anchor
Like a mini parachute this can be used to stop you drifting in the open water.
This is not an exhaustive list of kit and will probably be extended over time.