Ideally you should have everything we produce. Ok, we'll settle for a few standard items. At risk of sounding like a pimp, we make most of the wall stuff listed below. Other manufacturers make some great stuff too, and this is noted where applicable.
1. A large basic free rack.
This should include (for walls like the Nose or Salathe on El Capitan, the South Face of Washingtons Column etc) a double to triple set of small wired nuts, a triple set of cams to about #3, a couple of #4 cams, some extra free biners (the more the merrier), and some slings.
2. Specific aid hardware.
This is the stuff that you probably do not have in your standard crag arsenal.
Aiders: get two sets.
One set or using three is just not as fast or efficient. The people telling you that they use 3 or just one set are probably suspect. Ask to see their wall resume.
Daisy Chains: get two long ones.
You will need two for Jumaring and at least one while you lead. If you are doing any nailing or dicey hooking, you will use both while leading all the time. The shorter daises available are not very good for leading. They will work fine for Jumaring and for very easy and bomber aid. The fatal flaw of the short ones is you cannot reach over your head and place a piece with the daisy attached. This can be a problem.
Hooks: invaluable tool.
Even if you are on the easiest wall in the world, there will always be a place for hooks. If a bolt pops out of a bolt ladder, use the Leeper Bat Hook to get past the gap. If a big flake shows up while you are freeing out at your limit, plop a FISH hook on it for a needed rest. Use a Black Diamond Sky Hook for most of your basic hooking, as this is the most useful hook on the rack. For a multi purpose tool, take a Black Diamond Talon, another great hook.
Pulley: needed for hauling.
Drop the coin and get a Wall Hauler by Rock Exotica/Petzl. This unit includes a cam on the pulley so you don't need to set up the Jumar and pulley thing. Really good thing to have and will make your life much easier.
Haul Bag: mandatory unless you are going to knock off
your walls in a day.
Get a size suited to your needs. For most walls, a standard size of 9000 cu.in. is ideal. This size bag is great for a 3-4 day wall with two people. Another way is to take two smaller bags, like a Grade V size (5000+ cu.in.). This way you have a personal haul bag for each person and a bit more flexibility. Avoid the Haul Drum models now available. They tend to hang up a lot, and usually your first walls will be lower angle than some others, compounding the problem.
Stuff Sacks: for food, little items, rain gear etc.
Organization is the key. Food bags can be made for a daily grab or one big bag holding all the food. Get ones that are strong. You won't be disappointed with our Wall Bags or the Metolius versions. Both are durable and very strong.
Rain Gear: take it, even in summer.
Take the best you can afford. Being wet not only sucks, but can kill. If you are doing a wall that does not require a portaledge, take a bivy sack and maybe even a tarp. Cave as it sounds, a tarp is actually pretty good protection from the elements in a lot of situations.
The Little Things: these can make an epic casual.
A good headlamp with extra batteries. Gloves for Jumaring. Kneepads. Duct tape. A basic first aid kit. Aspirin or some other anti-inflammatory for "big wall fat hands" and stiff joints. A hat for the vertical desert. Sunscreen and lip balm. A Swiss Army type knife and extra eating utensils.