Many Beatles songs were either directly or indirectly inspired by real people, depending on how loosely you use the word "inspire." In my answer I'll assume you use it very loosely.

"A Day in the Life" was partially inspired by Tara Browne who "didn't notice that the lights had changed" and tragically died in a car crash in 1966.

"And Your Bird Can Sing" was possibly inspired by Marianne Faithfull, who was the girlfriend of Mick Jagger. She was the bird, and she can most definitely sing.

"Ballad of John and Yoko" was of course inspired by the real lives of John and Yoko. As absurd as some of the things sound ("eating chocolate cake in a bag") they were all things that John and Yoko did in real life.

"Blue Jay Way" was inspired by the Beatles' press-officer Derek Taylor who was supposed to arrive at George Harrison's house on a foggy night, but arrived very late. Garrison wrote this song while he was waiting for Taylor to arrive.

"Dear Prudence" was inspired by Mia Farrow's sister Prudence, who was meditating for several hours in India and wouldn't leave her room, hence the line, "Won't you come out to play?".

"For You Blue" was one of Harrison's few love songs that actually was written for his wife Pattie Boyd. (Contrary to popular belief "Something" was not written specifically for her.)

"Hey Jude" was written by Paul McCartney for Julian Lennon to console him after the divorce of his parents.

"I'm Looking Through You" was one of McCartney's many songs directed at his then-girlfriend Jane Asher.

"Julia" was inspired by Lennon's mother who died when he was a teenager.

"Lovely Rita" was the name McCartney gave to a meter maid who gave him a parking ticket.

"Martha My Dear" was inspired by McCartney's pet sheepdog, Martha.

"Savoy Truffle" was inspired by Eric Clapton, Harrison's friend who had an affinity for chocolates but hated the dentist. "When the pain cuts through your gonna know and how!"

"Sexy Sadie" was originally entitled "Maharishi" but Lennon changed it when he thought people would realize that it was directed at Maharishi Mahesh Yogi (duh...).

"She Came in Through the Bathroom Window" was inspired by a crazed fan who literally climbed up a fire escape to climb through McCartney's bathroom window.

"She Said She Said" (originally titled "He Said He Said") was written by Lennon after Peter Fonda (on LSD) repeatedly told him that he knows "what it's like to be dead."