Ryuuji Takasu has a huge crush on one of his classmates, Minori Kushieda, but hasn't been able to work up the nerve to talk to her, partly because everyone assumes he's a delinquent due to his shifty-looking eyes. It doesn't help that her best friend is Taiga Aisaka, known as the "Palmtop Tiger" for her short stature and hot temper. And it really doesn't help when he catches Taiga accidentally slipping a love letter to his best friend, Yuusaku Kitamura, into his bag. And it really really doesn't help when Taiga breaks into his house at 3AM to violently reclaim her letter.
Fortunately for all involved, this doesn't end in bloodshed but rather an uneasy truce, best described as "Ryuuji will now do anything Taiga asks him to, and in return might get to spend some supervised time with Minori". And so begins the quest to hook up Taiga and Kitamura, a task which leaves most of the school wondering what fresh terrors are in store now that the two most irrationally feared students suddenly appear to be dating.
This is just the setup premise for Toradora!; to try to explain the twists and turns both comedic and serious taken since then would rob you of the pleasure of watching them dynamically evolve through the first three volumes.
Our two protagonists are so destined to end up in a relationship that even their respective love interests comment on how great a couple they make. So it's fortunate that, individually, they're immensely likable and devoid of that artificiality that comes from the too archetypal character. Ryuuji is a paragon of domestic masculinity: his mother's entirely too flighty to properly take care of him, which has left him armed with formidable cooking skills and an obsession with cleanliness that borders on pathological—yet still has trouble finding friends due to his fearsome appearance. Taiga, meanwhile, uses her intimidating personality to mask her shyness and depression, and spends most of her not-school time listless by herself in her apartment. I find it easy to click with both of them on some level, whether it's with Ryuuji's (occasionally suicidal) devotion to those he cares about, or with Taiga's difficulty in properly expressing her feelings.
The secondary characters are just as likable, if not more so. Minori is perhaps the most persistently bizarre: she has about 200% more energy than the rest of the cast combined and does ridiculously outlandish things every time she shows up, ranging from making pudding in a bucket to revealing her true identity as a famed Diet-Soldier. Kitamura doesn't show up very often, perhaps due to his involvement with the student council, but whenever he does he usually joins Minori in her antics. Together, both of them boast an unusual perceptiveness towards Taiga and Ryuuji, often noticing their changes in personality before either of them do. A fifth major character, Ami Kawashima, doesn't show up until the second volume; a teen model on hiatus to finish school, Ami has perfected the sugary-sweet ditzy girl act that makes everyone like her, despite how cold and cruel she is on the inside.
What makes Toradora! stick out in my mind is the undercurrent of honesty behind the antics: the heartache, despair, and fear that various characters feel only surfaces a couple times in each volume, but they're always powerful moments and add depth to the humor, and in some cases overshadowing it. It's not unusual for a romance manga for boys to deliver this sort of depth and sensitivity—titles such as Kimagure Orange Road and Maison Ikkoku spring to mind—but it's not common. There's still places where Toradora! is clearly boys' manga—nothing attracts boys to romance manga more than attractive girls, not to mention that Ryuuji's mother spends most of her time in nightclothes—but it generally errs on the side of good taste. Ultimately, though, the biggest draw for Toradora! is that it balances comedy, drama, and romance without letting any of them overstay their welcome.
QUICK NOTE ON AUTHORSHIP: Toradora! is adapted for manga by Zekkyo from a 10-volume novel series by Yuyuko Takemiya. The three volumes of manga currently available in English cover approximately two of the novels. The novels were also adapted in 2008 into a TV anime series.