It all depends on how you handle the Barbarian class in your game. If you treat them as a cultural statement, instead of simple abilities and a way of fighting, it is hard to justify multiclassing for them.
I've often thought it was a mistake to call the Barbarian class by that name, since it holds cultural connotations that limit and restrict many peoples viewpoint of how a Barbarian comes about in a game world. Monks suffer a similar stigma, quite often, being restricted to aesthetic philosophers living in a monastery away from the rest of the world, basically becoming nothing more than Shaolin clones.
You can make a game world work that uses those classes in such ways, but I myself prefer to leave it more open. I can think of plenty of literary examples in fantasy books that would indicate someone taking a level of Barbarian.
Salvatore: Drizzt is a pure Fighter, up until the point he leaves Menzoberannzan and wanders off into the untamed wilds of the Underdark. Forced to rely almost purely on his instincts and learn how to survive in a harsh and unforgiving setting, he gains a level of Barbarian.
Tolkien: I'd say you could argue all five companions who are involved in the chase of the Uruk-Hai (Aragorn, Legolas, Gimli, Merry, Pippin) gained a level of Barbarian because of that. Aragorn, Legolas and Gimli had to run after the Orcs (who were clearly Barbarians themselves,

) across an incredible distance, and they actually managed to gain ground.
Merry and Pippin had to survive extremely harsh conditions when they were captured by the Orcs, and gained a lot of endurance and toughness because of that. I'd also argue that Aragorn, and probably Legolas and Gimli as well, had at least one or two levels of Barbarian before the chase began, making them already multiclassed Barbarians.
You could also argue Frodo and Sam gained Barbarian levels, but given their reliance on Gollum and lack of toughness (compared to Merry and Pippin at least) right up until the end, I'd say they probably remained an Aristocrat and Commoner.
Oh yeah, and Pippin and Merry clearly evidenced use of the Intimidate skill during the reclaiming of the Shire.
Brooks: I'd say when Morgan Leah attacks those Trolls and rescues Shirl, making a mad dash across rocky ground on his barefeet, while carrying a heavy load over his shoulder, he picks up a level of Barbarian in addition to his Ranger levels.
There's way more stuff I could go in too, here, but I really think allowing players to choose their own skills and abilities is best, and being a Barbarian is not a cultural commitment, it's just a set of abilities that help better define a character.