In Dungeons and Dragons 3.5

Rage says, in part,

While raging, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except for Balance, Escape Artist, Intimidate, and Ride), the Concentration skill, or any abilities that require patience or concentration, nor can he cast spells or activate magic items that require a command word, a spell trigger (such as a wand), or spell completion (such as a scroll) to function. He can use any feat he has except Combat Expertise, item creation feats, and metamagic feats. (PH 25).

That raging restricts other abilities requiring patience and concentration, but never specifies what those might be, means the DM has a free hand in declaring certain tasks require patience and concentration and therefore are beyond the raging barbarian. But the DM should probably rarely place such restrictions on tasks, given the limits present later in the description of rage.

Thus, as no mention's made of the raging creature being unable to do it, fighting defensively (PH 140) remains an option, as does total defense (PH 142).

It is odd, but the Player's Handbook just doesn't restrict rage beyond these limits. The game says that if it's not on this list (or specifically prohibited by an option in a later book), the barbarian can probably do it while raging; so it's perfectly acceptable for a barbarian, for example, to apply extra sneak attack damage if he has any, the target's vulnerable to it, and the circumstances mean he'd inflict it; fight defensively or use total defense; attempt disarms or otherwise use nonlethal force; and take the withdraw action.

The goal is to limit the raging barbarians' actions in exchange for increased combat prowess not precisely simulate violent psychopathy in a table top role-playing game. In this case an exclusive list is better than an inclusive list (i.e. the raging barbarian can't do these things versus the raging barbarian can only do these things) because the game knew dozens of books with far more options would follow, so rather than limiting the raging barbarian to actions--requiring every future option to note if a barbarian could use it while raging--, it prevents him from taking some actions, so the raging barbarian can use future options freely.

In Pathfinder

Rage says, in part,

While in rage, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except Acrobatics, Fly, Intimidate, and Ride) or any ability that requires patience or concentration.

And then omits the remainder. Without the rest of the list it's in the DM's hands as to what, exactly, requires "patience and concentration."

A cursory search of the skills turned up nothing explicitly requiring patience, in feats only the aptly named Patient Strike would seem to need it, and the bonus from a traveler's dictionary is increased if the user is patient. But the concept of concentration is loaded with meaning. Concentration is what's needed to cast spells ("To cast a spell you must concentrate"), for instance, and at least one use of the skill Use Magic Device requires concentration.

But the exclusions given for D&D 3.5's rage aren't otherwise present, so a raging barbarian can use Combat Expertise, magic items, and other D&D 3.5 restricted options if the DM rules these don't require patience or concentration. Thus it is up to the DM whether a Pathfinder raging barbarian can use the total defense action or fight defensively.

A barbarian/bard can, while in a rage, start and continue a bardic performance—maybe

The bard's bardic performances say nothing about concentrating and only a handful mandate Perform skill checks (countersong, distraction, et al.), making the others possibly usable while in a rage. However, performances do require using some kind of action to start and, often, to maintain. So while it's totally legit to get really angry and, for example, climb a mountain or swim a channel, because bardic performances use actions, starting or maintaining them while in a rage might run afoul of this part of the rage description:

While in rage, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except Acrobatics, Fly, Intimidate, and Ride) or any ability that requires patience or concentration.

Emphasis mine. So while the barbarian's rage itself doesn't explicitly forbid, for example, massive shredding on your lute or belting out "99 Bottles of Dwarven Ale on the Wall" while simultaneously furiously headbutting orcs to death, the GM can simply say No, starting and maintaining a bardic performance requires patience that's impossible while raging.

This GM would allow a character in a rage to start or continue an appropriate bardic performance

The player should be aware that it's a tough row to hoe, though. In addition to other issues like multiple ability score dependency,¹ the huge—perhaps, I dare say, insurmountable—problem with playing, for example, a barbarian 3/bard 4 is that such a character will each day have only a total of 11 rounds of fight in him (and that's generously assuming a Con 16 and Cha 16).² Level 7 is actually past the point when the wizard can cast an extended rope trick and everybody can rest in the extradimensional space in relative safety, so being good for only two fights per day (unless the group's really efficient) is fine at that point, but actually playing this character to that point would be a constant and—for me, anyway,—unpleasant war with an ever-ticking clock.

¹ Such a character needs high Str, Con, and Cha, would like a high Dex and Int, and will regret a low Wis.
² Yes, I'd put the extra level in bard. That means 2nd-level bard spells.