I am assuming you already have a repair kit for yourself... aka first aid kit, so I won't address that, but please see the thread from a couple months ago.
http://www.professorpaddle.com/forum/forum_posts.asp?TID=14182&EN=TU
As far as repair kit, it mostly depends on what you are bringing that might need repairing. Raft, kayak, or both? For a raft, you need a patch, glue, and a solvent to clean the area. NRS sells all of these, but they are specific to the raft material, so make sure you know what your raft is made of. You might also want to bring a valve-repair kit, as a leaky valve can be a serious PITA.
You should also have a sewing awl, which is good for fixing just about anything you can poke a hole though, such as sprayskirts, rafts, tents, river shoes, or even that hole in your underwear.
http://www.amazon.com/Speedy-Stitcher-T200-Sewing-Awl/dp/B000HGIJQ4
3mm accessory cord is just about the most useful thing you can bring, so bring lots of it. It's small enough to be compact and light weight, but quite strong, and pretty cheap. For a grand canyon trip, I would recommend at least 100', which you can probably find cheaper by the spool online. If something breaks, you can probably bind or tie it together with 3mm accessory cord. It's also great for setting up tents/tarps.
Next thing I would recommend would be tape. Duck tape is better for some things, gorilla tape better for others, so bring plenty of both. If you can't fix it with accessory cord, you can probably fix it with tape. You won't be hitting too many rocks in the Grand Canyon, but for a rockier river, I would recommend a good tape for kayak repair such as Vinyl-mastic, flexible window flashing, or some other industrial adhesive backed construction material. They are heavy, bulky, and expensive, but once it sticks, it's water tight for the rest of the trip (tape goes on the inside of the boat, but you can stick it on the outside too).
I would also recommend a few types of glue. Aquaseal is the most important in that it can repair your drysuit. Aquaseal also makes a UV-cure glue that is quite useful for fast repairs on a sunny day. Cyanoacrylate (AKA Super-glue / Krazy glue / whatever off brand you can get at the dollar store) is cheap, light and sometimes it's exactly what you need, so throw in several tubes (just make sure it's fairly new because it does go bad with age). I would also throw in a tube of 5-minute epoxy and some fiberglass cloth, which you can find at the hardware store, the autoparts store, or on the interwebs. Fiberglass/epoxy work in the field is rarely pretty, but it will fix that paddle, oar, or whatever enough to get you down the river.
The last things you are going to need are tools. A multi-tool will satisfy most of your needs, but you should have at least two in case you need both at the same time, or in case one breaks or gets lost. You should have at least: pliers, knife, scissors, flat-head screwdriver, phillips-head screwdriver, saw, and file.
Oh, and bring lots of tea-candles. Great for starting a fire with not-entirely-dry wood.
That's about it. You could bring everything under the sun, but when it comes down to it, there's not much you can't repair with string (thread and 3mm cord), tape, glue, a multi-tool, and a little creativity.
Have a nice trip,
Eli