The most important factors that determine what to wear for paddling are air and water temperature. However, you should also consider what type of paddling you are doing, and how long it could take you to reach help if you got into trouble.
Keep your noggin safe with a helmet designed for use in water, and dress with the assumption that you're going to get wet. You might be soaked by waves over the deck, capsize and roll, swim, or any combination of these.
Specialized kayaking helmets have large vents in the top or sides to allow water to disperse quickly and harmlessly. Trapped water can transmit impact shock directly to your head, including your delicate eardrums. If you're doing extreme stuff, consider wearing a chin bar or face cage to keep that grin on your face.
Keep your helmet away from hot places, such as the trunk of a car on a sunny day, as high temperatures can warp your helmet and reduce its shock absorption capacity. All kayaking helmets should be replaced in the event of a hard blow, even if the damage isn't obvious. The foam crushes to absorb impact, so one serious impact can make it ineffective.
For the coldest conditions (a glacial-fed river in nasty weather), a drysuit is the warmest, safest option. You may also want to wear a farmer john wetsuit and drytop, provided the drytop seals effectively around the waist to limit flooding (though this offers less protection if you swim).
Cold water and warm air are the trickiest conditions to dress for. Choose clothing that allows you to function for a while in the water, without overheating you in your boat.
Warm water and air make the most pleasant paddling conditions. If the water's a bit cool, you may want a short-armed, short-legged wetsuit. If not, rugged, quick-drying shorts and shirt, a good waterproof sunscreen, and your helmet, and you're off!
Unlike whitewater paddlers, touring/tripping paddlers do not intend to get wet. Still, the possibility of capsize must be considered. The higher the likelihood of capsize, and the more severe the potential consequences, the more protectively you should dress.
Consequences can mount if the water is cold, and if it would take a long time to get ashore. The time it takes you to get ashore depends on where you're paddling; if you're running a steep-banked river or paddling a rocky coast, the nearest landable spot may be miles away.
Keep your feet happy on and off the water.
Find out more about Paddling Footwear and Foot Care.