Unless the walk description says otherwise you should bring a packed lunch and plenty of water with you. How much water you need will depend on the walk, the weather, and how much you tend to drink, but not having enough water is unpleasant and, potentially, dangerous. Snacks and a hot drink can be nice too - the latter especially in winter. For harder walks you should bring additional food in case of emergencies.
Spare clothing is important - especially on harder walks. Remember to ensure that it is stored somewhere that will keep it dry (either a waterproof rucksack or dry bags are recommended).
For evening and longer winter walks a torch is a good idea, just in case things take longer than expected.
In the summer, please take, and use, sunscreen - no-one looks good when they're burnt or peeling. Remember, when you're outside for several hours you can still get burnt in March and September - even when there are clouds in the sky.
Please bring a change of shoes for after the walk, along with a bag to put your boots in. We usually go to a pub before heading back to Cardiff and, even if the pub doesn't mind you wearing muddy boots, the person giving you a lift might! Spare socks are also a good idea, as driving home in wet socks is not pleasant!
Other items you may want to bring include: a camera, a phone, a GPS (for recording where you've been), a first aid kit (plasters, bite cream, paracetemol, etc), wet wipes or hand gel, tissues, money, a map and compass (in case it's necessary to escort somebody back early, although you won't be asked to do this until you are known to be a competent map reader), and walking poles (but be careful how you use them - other people on the walk will object to having a walking pole in the face!).