Peanuts is well known for its use of the theme of unrequited love. Unrequited love is love that is not openly reciprocated or understood as such, even though reciprocation is usually deeply desired. The beloved may or may not be aware of the admirer's deep affections. The Merriam Webster Online Dictionary defines unrequited as "not reciprocated or returned in kind."
There are many characters in the strip who suffer from unrequited love, most famously Charlie Brown for the Little Red-Haired Girl. Other characters suffer from it as well, such as Peppermint Patty and Marcie for Charlie Brown, Lucy van Pelt for Schroeder, Sally Brown for Linus van Pelt, and Linus for Miss Othmar.
There have been many not so famous unrequited loves between other characters as well, such as Frieda for Schroeder, and possibly Snoopy for Marcie. Also, many minor characters have suffered from it, such as Cormac and Harold Angel for Sally, Floyd for Marcie, Tapioca Pudding for Linus, Royanne Hobbs for Charlie Brown.
One of the few romantic relationships in the strip that is not unrequited is that of Peggy Jean and Charlie Brown, who both liked each other--until Peggy Jean broke Charlie Brown's heart in her last appearence by telling him she has another boyfriend.
Linus and Lydia's relationship is also rather unusual in that it appears to be requited on both sides--but it usually plays out like an unrequited love story, with one attempting to get the other's attention and the other acting cool and indifferent. Sometimes Linus is the uninterested party, sometimes Lydia.