Unless the walk description says otherwise you should bring a packed lunch and plenty of water with you. Snacks and a hot drink can be nice too - the latter especially in winter (remember to pre-heat the flask before filling it with the hot drink as this helps keep it hot for longer).
Not having enough water with you is unpleasant and, potentially, dangerous. How much water you need will depend on the walk, the weather, and how much you tend to drink. I would suggest bringing 1l on shorter walks and 2l on the easier strenuous walks. If you are doing the harder strenuous walks you should have enough experience to know how much water you need.
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 within a normal rucsack are recommended - do not rely on rucsack covers as they can be removed in strong winds).
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.
Bring a rucsack or waist belt for storing the equipment you are not wearing or holding. It is much easier to carry items on your back with the load taken on your hips (as a good rucsack with a belt will do) than using your arms. Once again, using inappropriate containers for storing your equipment can make the walk a much less enjoyable experience.
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!).
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!