Duct tape. Lots of duct tape. You can use it to cover holes inside and out and wrap it around the hull for structural integrity. Tape over a leaky hatch cover and have a dry compartment again. Etc., etc., etc.

In the past, besides duct tape, I've also used screws, zip ties and different sizes of nylon cord. Know some basic knots because many times a good lashing can replace hardware.

Don't forget an emergency toolkit. I use a Leatherman with a Swiss Army knife for backup in case one or the other falls into the water. A piece of paracord makes a good lanyard, BTW, to keep your tools out of Davy Jones' locker.

All my emergency stuff fits into a small water-tight Otter box.

Finally, make sure that your knife is razor sharp. Better yet, take a razor knife. And when you get home, clean, dry and lubricate your tools.

Have fun,

Laszlo

Also, keep in mind that a patch does not have to be watertight. The leak just has to be slower than what you can bail while underway.

Laszlo 

 +1 on Lazlo's suggestions.  Marathon canoe racers also carry a small can of lighter fluid and a lighter.  If they get a hole, they spray the area with lighter fluid and light it on fire to quickly dry the area so that the duct tape sticks.  Gets them back in the race more quickly.  Personally, I use Gorilla Tape.   

My earliest foray in a kayak – skin-on-frame – left me with the memory of being 'landed' on the far shore with a hole punched from an unexpected encounter with a tree limb hauling out for a break.

Duct tape got me back across the lake in good stead.

Don't leave shore without some.

Or the more modern stuff that's maybe even stickier & will maybe work on a wet surface.

(Wouldn't alcohol be safer than lighter fluid for 'flashing' off moisture?) 

Mark,

That reminds me of a Marine DI who told a bunch of us kids in a high-school health class of how Marines get rid of lice - with lighter fluid, a razor, a bayonet and a match.  Shave off 1/2 the affected hair, soak the rest with lighter fluid, set it on fire with the match and stab the critters with the bayonet as they run out on the bald spot to avoid the flames.

Laszlo

That fit's with my understanding of Jarhead philosophy Laszlo..."What doesn't kill me only makes me stronger." 

   I served with a few guys that follow that philosophy. 

I guess we Army grunts are a bit more tame. In Vietnam, a drop of mosquito repellent and those leeches couldn't let go fast enough.