The next part of my general Core fix is boosting the barbarian. Barbarians don't need much boosting, but they are still uncomfortably close to a melee-optimized cleric or druid, so a bit more is needed.
Therefore, the boost consists of giving the barbarian a special ability at 10th level, and once every 3 levels afterward (just like a rogue). The barbarian's abilities can be chosen from the following list. Unless otherwise noted, these abilities may only be used when raging and each one may only be taken once:
If the barbarian attempts to begin a grapple, and the provoked AoO does damage, he may make a Fortitude save, with DC equal to the damage done, to continue with the grapple anyway. In addition, the barbarian gets a +4 bonus to his grapple checks, increasing to +6 at level 11 and +8 at level 20.
The barbarian may, as a full-round action, lift above his head an item weighing up to twice his maximum load. The following round, he may spend a full-round action to throw the item as an improvised thrown weapon.
This requires an attack roll, with a penalty depending on the weight of the item: An item weighing up to the barbarian's light load takes only the -4 penalty for an improvised weapon, an item weighing more than his light load takes an additional -3 penalty for -7 total, an item weighing more than his medium load takes an additional -3 penalty for -10 total, and an item weighing more than his heavy load takes an additional -5, for a total penalty of -15 to the attack roll. An item larger than the barbarian himself always takes the full -15 penalty.
If the item hits, it does damage as though hurled with the Telekinesis spell (if it is too heavy to be hurled with that spell, it deals the damage such an item would do if it were possible).
A barbarian with both this ability and the Grappler ability may, as a full-round action, use a Grapple check to lift a grappled creature no larger than himself above his head (provided its weight is not too high); if the creature does not escape by the next round, he may throw it as he would throw an item.
If a thrown item hits a structure or structural feature that is not freestanding, it does no damage. Instead, the item makes a strength check to break the item, with an effective strength bonus equal to 1/10th the damage it would have done (rounded down). If the barbarian has the Break Item special ability, the bonus from the ability applies to this roll.
The barbarian adds +2 to strength checks to break items. This bonus increases to +3 at level 11, and +4 at level 20.
Improved Power Attack:
When the barbarian uses the Power Attack feat, he adds 25% to the total damage increase from the feat. This ability may be taken more than once.
Battle Rush (borrowed and slightly modified from Ashtagon's idea in this thread):
If the barbarian inflicts melee damage to an enemy that threatens him at the beginning of his turn, he gets temporary hit points equal to half the damage done. These temporary hit points are lost first as usual, and automatically vanish at the end of the rage.
If the barbarian's hit points are equal to less than the amount gained from his rage through an increased constitution score, then the bonuses to Strength and Will saves from the rage are doubled for as long as this state lasts. Numerical bonuses from the Grappler and Break Item abilities are doubled as well.
If the barbarian is at 0 or fewer hit points, he may make a Fortitude save, with DC equal to the negative of his hit points, to resist all effects of his low hit points (being disabled, dying, or dead). Even if the Fortitude save succeeds, any strenuous action still deals one point of damage, as it would for a disabled character or a dying character with the Diehard feat. He must make the Fortitude save every time he takes damage (including the damage that puts him at or below 0 hit points), as well as once per round at the beginning of his turn. For purposes of this ability, nonlethal damage is treated as if it were a direct reduction of the barbarian's hit points.
Feat: A barbarian may gain a bonus feat instead of an ability. This feat must either be Power Attack or have Power Attack as a prerequisite, and applies even when the barbarian is not raging. This choice may be taken more than once.