They would be...

Clannad
Air (This touched my heart the moooosssttt-est)
Bokura ga ita
Saikano
Ano Hana (This touched my heart the most!)
Kimi ni Todoke (This touched my heart the mooooossssttt-er)

I can't think of any more animes that touched my heart. Maybe because I'm sleepy.. But actually, all the animes I've watched touched my heart. HAHAHA.