When it's time to replace your 4x4 truck tires, you'll find that you're faced with several options. Which type of tire is best for your vehicle will depend on several factors.
The first thing you'll find is you can choose between mud tires and all-terrain tires. Most 4x4's come with all-terrain tires from the factory. The tread pattern on these tires is designed to give you reasonably good traction on most surfaces, but they're really made for street driving more than anything.
Aftermarket all-terrain tires, like the BF Goodrich All-Terrain T/A for example, will make a big improvement in traction on off-road surfaces but you will find they run a little rougher on the street. If you do a lot of four wheeling, this can be a good trade-off between street performance and off-road performance.
Mud tires, such as Super Swampers, have a much more aggressive tread pattern. The treads are quite knobby, with wide spacing to allow mud to clear from the tread. This gives much better performance for off-road use (even on surfaces other than mud) but it makes for noisy, rough rides on the street.
Mud tires will also wear a lot quicker if you do much street driving, so this is something to consider. If your 4x4 is your daily driver as well as your off-road vehicle, it can even pay to have two sets of wheels and tires so you can swap them out when you're going four wheeling.
There are various sizes of 4x4 tires, from the standard sizes that come from the factory on most vehicles to monster truck style tires that require a big lift and fender mods to fit. In most cases, somewhere in the middle will be your best option. Something bigger than the original tires will give you better off-road performance, but unless you want to spend big bucks modifying your vehicle, you don't want to go too big.
When you're shopping for tires, most major brands like Goodyear, Hancook, Cooper and Firestone have off-road tires available. But you can also get house brands at most larger chain tire stores, and these brands often have better warranties. Some even cover the tires against any kind of damage, so if you hit a rock somewhere and tear the sidewall up they'll just replace the tire for you.