Instead of a clever attempt at a plot summary, I'll defer to ANN's:
“When timid eleventh-grader and math genius Kenji Koiso is asked by older student and secret crush Natsuki to come with her to her family’s Nagano home for a summer job, he agrees without hesitation. Natsuki’s family, the Jinnouchi clan, dates back to the Muromachi era, and they’ve all come together to celebrate the 90th birthday of the spunky matriarch of the family, Sakae. That’s when Kenji discovers his “summer job” is to pretend to be Natsuki’s fiancé and dance with her at the birthday celebration. As Kenji attempts to keep up with Natsuki’s act around her family, he receives a strange math problem on his cell phone which, being a math genius, he can’t resist solving. As it turns out, the solution to the mysterious equation causes a hijacking of the social networking site through which most of the world's social and business traffic flows.”
The subplots of the fiancé charade and Sakae's birthday aside, anyone familiar with the second of Mamoru Hosoda's two Digimon short films, Our War Game, will notice more than a passing resemblance to Summer Wars; this is compounded further by the look and developments (especially the climax nearly replicating the big twist and comeback!) of the two movies. Sadly, this does result in somewhat derivative moments -- even though in Summer Wars they may better those in Our War Game -- and perhaps more crucially, misses the urgency of the Digimon film. The plot is more than enough for the concise forty minutes of Our War Game, but lacks the intricacies needed to be fully satisfying when it's extended to over one hundred.
Then again, I thought Paprika was one of Satoshi Kon's lesser works, before on a second re-watch came to feel that it's his best film. Who knows how I'll see my current misgivings of Summer Wars later on?
Regardless, that's where the negatives primarily end, as it's the characters and ideas that hook themselves in your mind. While I empathize far more with Makoto (The Girl Who Leapt Through Time), Kenji's position as an awkward but principled nerd is shown quite honestly; his latent proactive attitude is the result of his own personality and talents, rather than arbitrary plot mechanics. Satsuki, while not as well-defined as Makoto, actually behaves like a real teenage girl, carefully nuanced (considerate, selfish and brave are just a few adjectives that can be applied) and developed over the course of the story. Her family is even better, with the grandmother, Sakae, being on the short list of nominees for Best Character of All-Time in animated film. She's the very embodiment of charisma, order and understanding, and also represents the film's key themes (the importance of connections, comprehending the extent of one's abilities and acting on them, and the meshing of the traditional and contemporary) in vital ways: her two important conversations with Kenji about his relationship with Natsuki; the order and invigoration she instills in the seemingly countless important workers and public officials across Japan as they deal with the Oz Crisis, never mind her family; and her mindful awareness of the family's history (both of centuries past and the present generations) and how it should be acknowledged in the future (her relationship with Wabisuke is most representative of this, with the information doled out at the most appropriate times). The rest of the family is admirably diverse and free of stereotypes, most of them well-defined based on just a few lines of dialogue, their posture, attentiveness (or lack thereof) to the situation at hand, et cetera. They're portrayed so authentically that my mind started linking all sorts of associations to my own friends and family (both the good and the bad!). Some are attuned to modern technology, others less so or not at all; in fact, the one most involved is Kazuma, a reclusive thirteen-year-old male that provides the most immediate help to Kenji, and who has his own growing pains to deal with (before and during the movie). It's the entire cast’s personal tics that engages the viewer for the first hour, and also stir the viewers through the action-oriented second half.
Oh, yeah, and there's the visuals. As with the story, Hosoda borrows and refines many of the visual ideas from Our War Game, but with greater, more consistent success. Even though they never reach the sheer plain of pleasure of the sixth One Piece movie, Hosoda... well, screencaps do a far better job than words (no actual spoilers):
Very different than the subdued tones of The Girl Who Leapt Through Time, but very vibrant, well-composed work that gives a good sense of weight and motion. Wonderful stuff.
What's the most endearing aspect of the film, though, is one that should receive plenty of thought by viewers after the credits end. In fiction, the negative side effects of technological progress (environmental degradation, alienation amongst a sea of people, deepening issues of classism) are almost always given without much, if any reflection of the positives. Summer Wars adds this much-needed perspective where this greater ease of communication allows us an astounding amount of information in mere moments, the ability to connect with friends and family that we haven't seen or spoken to in years, and even save lives. The potential for cooperation and deep, transcultural relationships is there -- it's on us to reach it. It's an optimistic point that we need reminding of more often.