Twin Spica starts out dramatically with the crash of a rocket on Yuigahama and keeps it up for most of the series. Sure, there is some light-hearted material too, but the tearjerking moments prevail throughout. One of the saddest stories in the anime is told during the flashback about Asumi, her first love Takashi and the big Sakura tree. This troper wept. Hard!
This troper wept highly and mightly with Lion-san's backstory, about how he indirectly asked Ms. Suzunari's (who is also Asumi's teacher) hand in marriage the day before the accident that killed him. And how she only noticed that the wedding ring was inside the keychain several years later, and crying over that. It was sad in every single page of the manga chapter, and every single second of the anime episode.
And let's not forget the part of Asumi's backstory with her childhood near-death experience. It's covered by episode 5 in the anime. This episode would make CHUCK NORRIS CRY.