Most cats are not particularly happy travelers - they are usually bonded strongly to their own territory and feel very vulnerable in a new environment. The rewards of staying with the family and heading off on an adventure does not excite the average feline in the same way as its canine cousins. \
If you wish to take your cat on a train/car or air journey you will have to ensure your cat is safely and comfortably secure in an appropriate carrier and is kept confined at the end of the journey, at least until comfortable in the new environment. Of course you get the occasional cat that travels frequently with its owner and does not panic or run off in a new environment, however, these are few and far between.
Traveling by Car
It can be very dangerous to have a cat loose in the car - not only could it cause an accident by becoming entangled with the driver, but if a window or door was opened or an accident occurred, the cat could escape and become lost.
You will need to invest in a carrier that is strong and easy to clean should the cat urinate, defecate or become sick during the journey. Also consider the weather you will be traveling in - both your present situation and the likely temperature of your destination. If it is likely to be very hot then use a carrier which allows good air flow - if it is going to be cold then one which can provide draft-free warmth while still allowing a good air flow would be useful. Place the carrier where it will be secure if you have to brake suddenly but where it has a good air flow - i.e. not underneath lots of other luggage in the back of the car. Do not put the cat in the trunk and take care with the rear of hatchbacks - ventilation may be poor and your cat may overheat. You can secure the carrier behind one of the front seats or use the seat belt to make sure it is held securely on the seat.
Check the cat regularly, especially if the weather is hot - don't underestimate how rapidly the temperature inside a car can rise - bear this in mind if you stop for a refreshment break and leave the cat in the car. Put the car in the shade and leave windows open - if it is very hot take a picnic and eat it nearby with the cat secure in its carrier outside the car or with all the doors open. Heat-stroke can be a killer.
Traveling by Train
Obviously if you are traveling by train you will need a very secure carrier which the cat cannot possibly escape from, but one which is also light enough to carry. You may want one with a solid base in case the cat urinates so that it does not soil the railway carriage. Line it with absorbent paper and material and take spare bedding too. You will probably be able to keep the cat in its carrier on your lap depending on the type of train and the space available.
