Just like dogs, cats can be trained to walk on a leash. It will take time and patience, but it can be done.
There are great benefits to training your cat to walk on a leash.
With greater emphasis on keeping cats indoors and safe (from traffic and predators), many cats would not otherwise get to enjoy the great outdoors, unless they are provided with a cat enclosure.
Training your cat to walk on a leash is easiest when the cat is young. It will need to be done slowly, in order to have any chance of success.
It is not recommended that you use a standard collar and leash on a cat as they can easily wriggle out of the collar if panicked. It is recommended you use a harness (see picture above), which come in a number of shapes and sizes. The harness and leash should be lightweight and comfortable.
Start out by putting the harness on your cat for short periods of time. This will allow him to get used to the feel of the harness. The harness should initially be placed loosely on the cat, and over time slowly tighten it until your cat is comfortable wearing the harness properly fitted, you should be able to fit two fingers between the harness and the cat. Extend the amount of time your cat spends in the harness. If your cat panics, back off and try again another day. Do not force the harness on a stressed or upset cat.
Once your cat is comfortable wearing a harness, attach the leash and try walking around indoors at first. Do not pull on the cat, rather let the cat guide you.
Once the cat is confident to walk with the harness and leash in the safety of your home, slowly introduce him to the outside world, preferably in the garden, if you have one. Avoid busy and noisy areas as this will stress the cat. Start out on short walks, and let your cat give you feedback. If he is scared, bring him inside and don't force the issue.
Some cats will happily walk on a leash, others won't. Patience and persistence are required, but if after several weeks or months, your cat still hasn't accepted the harness, it may not be worth forcing the issue. Siamese, Orientals, and Bombay cats are all said to be quite adaptable to harness training.