Here are Sam's, Rogil's, and Kathy's lists of canyoneering supplies all in one.
Wetsuit: highly recommended for the Black Hole, which requires swimming through long stretches of very cold water. Sporting-goods shops have lightweight wet suit tops. Some people use wet suits that are minimal (tank top and shorts) or a light Neoprene shirt. Most common in our group is a shorty wetsuit from Popular, about $50.
PFD (life vest): provides insulation around the chest area as well as flotation and helps keep your chest out of the water; recommended for any slots that require swimming; also recommended, in addition to the wetsuit, for the Black Hole.
Drybag(s): essential to keep equipment, clothes, and food dry; also works as a flotation device. Sam likes the SealLine drybags from Cascade Designs. None of his SealLine bags have ever leaked. Get a drybag that will fit inside your pack; Kathy recommends that you put grommet holes in the bottom of your pack to let water drain. Or get a drybag pack; ask Rogil about drybag packs, since she's had experience with leakers.
Neoprene socks or booties: Rogil suggests wool socks. If you're interested, ask Kathy for a big, long email discussing how to keep feet warm in ice cold water (although her hands were colder than her feet on the 1998 Black Hole trip).
Boots for wading, swimming, and scrambling: Sam says approach shoes work pretty well. For most of the slots we've done, changing shoes for each activity is not practical, so you'll be hiking and swimming in the same boots. Rogil suggests below-the-ankles hiking shoes so you can swim and still have your toes protected. Kathy chooses shoes based on the trip: trail runners when traction is more important and boots with ankle support otherwise. Some boots shrink when they dry; stuff them with newspaper to keep their size and shape when drying.
Hiking stick(s): for wading in streams with slimy rocks and potholes; any stick (e.g., broom handle) that won't give you splinters will do. Walking sticks are a necessity for wading in many creeks or rivers (e.g., Zion Narrows, Wet Beaver Creek, East Clear Creek), both to help you stay standing against rushing waters, to avoid slipping in goo, and to help with rock hopping. Walking sticks also allow you to check the depth of pools and mud. For trips that involve swimming, a stick that will float is good.
Water filter and/or purification tablets: the water in most deep narrow canyons is highly suspect and sometimes has dead creatures floating in it. (Some is too silty to filter, so don't rely on filtering or tablets.)
Nylon pants/shorts: they still provide some warmth when wet and dry quickly. Avoid any cotton clothes in the slots; once cotton gets wet, it takes a long time to dry and you'll freeze (we've had people close to hypothermia on past trips, even in the summer). Rogil and Kathy usually wear nylon pants for protection from brush and sun. Kathy prefers to have zip-off pant legs (REI brand).
Coolmax or long underwear top: quick-drying synthetic shirts are best. Rogil likes to wear a long underwear top and unzip it between swims to keep from overheating. (Some people wear a paddler's vest the same way.) See "Nylon pants/shorts."
Headlamp: some past day trips have taken longer than we planned; be prepared for that.
Very light wind breaker: to wear in or out of the water. Kathy almost always hikes with a packable windbreaker, rain coat, and rain pants (after being unexpectedly stranded in a slot canyon once).
Broad-brimmed hat: for protection from the sun and some warmth.
Towel and dry clothes: good to have in your pack as emergency gear in case you over do it. Have dry clothes and shoes to change into after finishing wet hikes, too.
Rappel gear: harness (or 20-foot sling for swami belt), helmet, locking biners, belay and rappel device, gloves (if you want), and prusiks (or ascenders?). Analyze the trip description to see if you think this gear would be a good idea.
Anchors, ropes, slings: for rapelling, belaying, lowering packs, etc. We may need to donate some slings and rappel rings to rappel stations. Analyze the trip description to see if you think this gear would be a good idea.
Helmet: head protection is a good idea in canyons requiring a lot of vertical work. For example, the Blue Springs "trail" is so vertical at the beginning that it's very easy to knock rocks down on the rest of your hiking group. You should always bring a helmet when rappelling is expected.
Water: parts of the hikes will probably be hot. The Hiker's Guide to Paria Canyon says, "In hot weather, carry a minimum of 4 quarts of water for each person per day." Do not take this lightly. BRING PLENTY OF WATER! Make sure it fits in your pack with all your other stuff.
Food: you'll need at least snacks and lunch for the hikes. If we do any hard hikes, you'll need extra calories. You'll need breakfasts and dinners for in camp, but hopefully we'll eat out for dinner as often as possible.
Maps, compass, GPS, route description: if only we knew where we were going....
Gaiters: not necessary, but helpful to keep tiny, stirred-up rocks from collecting in your shoes on some wading hikes.
Soap and water: to wash off poison ivy oil.
Standard hiking supplies: see the checklists.
Camping supplies: we'll probably be camping with NO FACILITIES for most, if not all, the nights of our trip. You don't have to backpack your stuff. Even in May and June you should be prepared for both hot and cold camping (shorts, sleeping hat, gloves, warm jacket); we'll probably camp at both high and low elevations. Bring dry clothes to change into after wet hikes.
Shower supplies: we might try buying shower tokens at a real campground, so bring stuff for taking a shower (towel, soap, etc.).
Large watertight cannister: to keep things dry and unsmooshed.