At the end of "The Great Unwashed", Jenny feels down because she's been kicked out of Don Prima's party which she spent the whole episode trying to get invited to and preparing for. She mopes by herself until Brad and Tuck start a water fight with her and she has fun with her friends.
A relatively minor example, but after Jenny saves the Crust Cousins when the lab catches fire (Which they caused in the first place by launching a hairpin into her laser arm) they stand up for Jenny when the principal tries to have her arrested, calling her a hero and letting her hang out with them. It's subverted a moment later when Jenny finds the hairpin and the principal recognizes it and has them arrested, but even if it was only for a minute, it doesn't change the fact that the Crust Cousins did genuinely want to be friends with Jenny
In "Daydream Believer" when Jenny asks her mother if she can experience what it's like to dream, Mrs. Wakeman says that she'll consider putting the idea of a dream-chip on her very long list of things to do. Jenny feels sad, believing that she'll put the idea at the very bottom; she instead makes it the very first thing to do on the list.
In "Puppet Bride" Mrs. Wakeman saving Jenny from Little Acorn saying she won't let him take her daughter as his bride showing that she does think of Jenny as more than a mere robot.
A fan asks Rob to sign a rare piece of memorabilia, and Rob replies, "Oh, yeah, I remember that; I'll just send you one of my own." Then he sends not just his own autograph, but the signatures of all the fellow animators he could findnote Rob Renzetti is currently working on Disney's Gravity Falls, and a good portion of Teenage Robot's crew also migrated over to the company, so it was easy for him to find them as well as another poster for the TV Movie, signed and thanking him for being a "true" fan.