Every cat is at risk of developing worms at some point in its life.
There are two main groups of worm in cats: roundworms and tapeworms. Some types of roundworm are passed to kittens from their mother, so all cats can be infected. Some of these worms can remain as dormant larvae for years. While dormant, they are not killed by worming treatments. These worms can become active later in life and can possibly be passed to children.
Most types of roundworm live in the gut, and unless there are lots of them, they generally do little harm. If numbers build up a lot (especially in kittens), they can obstruct the gut and are a very serious problem. Lungworms are a type of roundworm, and can cause breathing problems.
Tapeworms are picked up from eating "carriers" (intermediate hosts). These can be fleas or prey such as mice and rabbits etc. Tapeworms are rare in kittens and virtually never found in cats which have very effective flea control and do not hunt. Good multi-wormers will kill all types of worm in one dose.
Cat wormers available from VioVet WITHOUT A PRESCRIPTION -
TermaWorm - TermaWorm™ Tablets for Cats & Dogs are our own brand worming tablets, intended for the treatment of all common roundworm and tapeworm found in the UK. 
Panacur - Safe and effective for roundworms, but not great for tapeworms. Best given daily for 3 days - especially good this way for kittens or adults showing any illness due to worms. Available as granules to mix in food, or liquid or paste to give directly into the mouth.
Granofen - same ingredient as Panacur above (fenbendazole), same results.
Drontal Cat - Very good product, safe and effective against roundworms and tapeworms in one tablet.
Droncit Spot On - Very easy to use, very effective for tapeworms, but NOT EFFECTIVE for roundworms.
Bob Martin Clear Wormer - Very easy to use, very effective for tapeworms, but NOT EFFECTIVE for roundworms.
PRESCRIPTION ONLY PRODUCTS -
Milbemax - safe and effective for roundworms and tapeworms. Very small tablet so easier to administer.
Advocate - kills fleas, roundworms, ear mites and lice but NOT EFFECTIVE for tapeworms. A spot-on medication, making it easy to use for most cats.
Stronghold - kills fleas, roundworms, ear mites and lice but NOT EFFECTIVE for tapeworms. A spot-on medication, making it easy to use for most cats. Containing a different ingredient to Advocate above but similar in properties.
For full information on each product, see the datasheet listed in the product description. If using non-prescription products, VioVet recommend TermaWorm or Drontal for worms, and Frontline Spot-on or Fipnil or fleas. These are as safe and effective as the prescription products. If using prescription-only products, talk to your vet about what they recommend, but you are welcome to email VioVet with any specific questions.