The "improved" versions are feats which allow you to ignore Attacks of Opportunity. Without these, you not only become vulnerable to a free attack upon yourself when using them, but also the opportunity to be knocked out of them via this attack as well, preventing and wasting the action entirely. As such, it's best to not even consider the maneuvers as possibilities at all without the improved feat or in the most dire of situations.
When building a melee character that uses these abilities, make sure to consider the Intelligence Requirements of Combat Expertise, which is a prerequisite of several of them. You need an Intelligence of at least 13, something Barbarians are not known for having without planning and forethought.
Many of the maneuvers are very situational, but useful in these specialized conditions. Here are some times where their use is at their extremes of advantage or disadvantage:
Tripping is extremely powerful against humanoid creatures with two legs, save for Dwarves (who have an ability specifically to counter it). In an adventure mostly against humans and humanoids, it can cripple enemies of most any level, although melee fighters have some resistance to them. Against almost any other enemy type, however, its usefulness drops drastically. It is all but useless against anything with four or more legs, anything without legs, anything bigger than you, anything incorporeal, or anything with a substantial enough acrobatics score to simply stand back up unhindered.
Disarming is also similarly very useful against humanoid creatures that use weapons, and very non-useful elsewhere. Many humanoid creatures, like player characters, are built to require weapons and possibly specialize in them, making them a nice weakness to exploit. Against other creatures, however - aberrations, ghosts, giants, dragons, what have you - it's useless. Against weaker creatures like goblins and kobolds, of course, you're better off just killing them instead.
Bullrushing is very useful for manipulating the battlefield, and its limits are based less on the type of enemy and more on the terrain. Simply put, you have to have a location to push someone into, and a reason to do it. Use it when you believe you can use the terrain to your advantage in some way. An enemy's resistance to it is based off strength and size, so big enemies will be tougher to push, but as a barbarian, you may be able to best many foes in this area if you rage first.
Sunder is a tough sell in any situation, since the items you are sundering are generally also your treasure, and a hefty part of your monetary income. With that disadvantage in mind, it is useful in nearly identical situations as disarm. Use with proper judgement.
Charge is possibly the most universal ability to keep in mind. It does not require a feat to use properly, and only needs to be weary of its natural counter: reach weapons. Charge sacrifices defense for offense, as well as allowing you double move and attack, so long as you can do so in a straight line (doesn't have to be directly orthogonal on the grid, just a direct line at any angle) that avoids rough terrain. As a barbarian, this ability will allow you to do some very heavy offensive pressure, if at a slightly higher risk. It puts you in the enemy's face and forces them to respond, in any case. It is equally useful against almost all enemy types, and its terrain limitation is fairly small. Barbarian Smash!!