I know it's been over eleven years, but after reading the last post, I beg to differ.
Warning... major spoilers ahead.
The titles of the books are formulaic... Harry Potter and the (fill in the blank). Since the titular character name "Harry Potter" and the linking words "and the" are always the same, the significance of the remaining words of the title reveal to us the intent of each book.
Harry Potter and the Philosopher's Stone. We find out that the philosopher's stone is a magical item that allows a wizard/witch to continue to live without aging, e.g. a fountain of youth. The book might just have as well been titled
Harry Potter and the Life.
The book opens with muggle life and Harry's appearance upon the Dursley's doorstep... a fundamental life change. We see Harry's neglect and abuse by the Dursley's... a poor quality of life. We see the revelation of his abilities and his place at Hogwart's... a new life. He makes friends... a hopeful life. He makes enemies... a dangerous life. He gets nourished, not only in body, but in mind and spirit... a fulfilled life. Snape hates Harry because of James and Sirius... a frustrated life. Voldemort is stuck to Quirell... a half life.
The Mirror of Erised is not just a fanciful invention. It clearly expresses Harry's heart's desire... a father and a mother, love, encouragement, understanding, and a sense of belonging.
The questions regarding quantity and quality of life abound. Is one more important than the other? Physical survival must be continually secured, but success and significance must be consistently pursued. Faithfulness, family, and friends are all necessary to a high quality of life... and Harry lacked these at the Cupboard Under the Stairs, Number Four, Privet Drive, Little Whinging, Surrey.
As for the other books...
Harry Potter and the Chamber of Secrets. The Chamber of Secrets is hidden in the heart of Hogwarts with the purpose of revenge. Everyone in this book has a secret... the Dursley's, Harry, Mr. Weasley, Percy, Lockhart, Hagrid, et al. and they don't want to be found out. They bury their secrets in their hearts... the chamber of secrets. What effect do secrets have? Major impacts upon our quality of life. The book could have been titled
Harry Potter and the Heart.
Harry Potter and the Prisoner of Azkaban. Sirius is the prisoner, but he's more a prisoner to his hatred and lust for revenge than Azkaban. Buckbeak is a prisoner. Harry, Snape, and Lupin find themselves caught up in James' and Snape's rivalry for Lily's affections even though close to twenty years have passed. Dudley and Draco are practically hostages to their family's values. Lupin is a prisoner to his affliction. Pettigrew is a prisoner in his chosen form. Psychological prisons can be just as restricting as prisons from life choices. Book three could have been called
Harry Potter and the Captive Spirit.
Harry Potter and the Goblet of Fire. The goblet of fire signifies a passionate high stakes competition. The House Cup is put on hold while the tri-wizard tourney, the Quidditch Cup, death eaters versus muggles, Voldemort's and Crouch Jr.'s versus Dumbledore's plans, Harry's and Ron's friendship, Hermione's and Ron's friendship, Hermione versus Rita Skeeter, and Harry's duel with Voldemort are plainly more important and relevant life issues. Could have been
Harry Potter and the Far-Reaching Struggles.
Harry Potter and the Order of the Phoenix could have been titled
Harry Potter and the Life Partnerships. The Order of the Phoenix is a dedicated club to never rest against Voldemort's terror. Various organizations exist throughout the book. Dudley's gang, the Ministry of Magic, the Dementors, the Death Eaters, the Order of the Phoenix, the quidditch teams, the prefects, Dumbledore's Army, the Inquisitorial Squad, St. Mungo's, the Giants, the House Elves, the Centaurs, Hufflepuff, Gryffindor, Ravenclaw, Slytherin, the Daily Prophet, the Quibbler, the Dursleys, the Malfoys, the Blacks, and the Weasleys are all groups, clubs, businesses, schools, associations, ethnicities and governments to which characters can belong. JKR, in no uncertain terms, writes that who we align ourselves with matters a great deal. This is most strongly represented by the six who go on the rescue mission.... Harry, Hermione, Ginny, Luna, Neville and Ron. And the inclusion of the phoenix, a symbol of rebirth and new life, in the battle of good versus evil is surely more than coincidence.
Harry Potter and the Half Blood Prince. The Half Blood Prince is a secret childhood identity for Snape and the theme of the book is identity. The book opens with Snape's revelation of his involvement with both sides up to his neck. Harry is captain. Draco is a death eater. Fred and George are brilliant at odd ball magic and business. Harry's connection to his father has always been strong, but here he's constantly compared to his mother. Harry and Ron discover girls. Harry has always been the Boy Who Lived, but now he's the Chosen One. Harry gets a reputation as a potions genius. Harry gets special lessons with Dumbledore. Ron gains more of a reputation as a quidditch player. Twice, Harry claims to be "Dumbledore's man." Harry becomes a searcher for horcruxes. At the end of the book, Harry has decided to quit school, embrace his identity, and pursue Voldemort's demise. Ron and, to my great surprise, Hermione also quit school and join Harry.
And what we ultimately learn in the seventh book makes Harry reconsider Snape's identity to such an extent that he names his second son after Snape!
Harry Potter and the Deathly Hallows. Revered objects associated with death. Just as the theme of the first book was life, the theme of the last is death. But life and death are linked. You cannot have death without life. You can have life without death.... but that is beyond this mortal plane in which we now live.
The wand. The stone. The cloak. Individually, they provide a boost to the quality of life. Ron would choose the wand, Hermione the cloak, and Harry the stone. Collectively, they make the owner the master of death... i.e. they give life. But is life for life's sake to be more highly prized than the love found in life? This is the very difference that Dumbledore tries so hard to impart to Harry. Voldemort want's life so he'll never have to die. Dumbledore wants a life of love. Harry sees this consistently in his friendships with Ron, Hermione, Luna, Neville, Hagrid, Sirius, Lupin, Ginny, Fred, and George. The Weasley family imprints such love of each other and their love for truth upon Harry so much that he marries into the family.
(I think JKR should remember this before saying Harry and Hermione should've ended up married. Harry's desire was not for a witch with equal abilities, nor a brainiac, nor a great heroine... but for a loving family. Now, he got an outstanding witch [the only two non-well connected students to be included in the Slug Club were Ginny and Hermione, both chosen for their outstanding wandwork and character] in Ginny... brave, heroic, intelligent, humorous, and loving. And I feel the entire Weasley clan was attractive to Harry.)
Anyway, back to the point... Harry is faced with the decision to pursue Hallows of Horcruxes. His own power, his own life versus the destruction of Voldemort and the betterment of society. Harry finds out there are things worth dying for... and he embraces this philosophy. And he honors those who died in the struggle to defeat Voldemort in the very names of his children.
James (three times foiled Voldemort, willingly laid down his life for his wife and child, murdered by Voldemort)
Sirius (renounced Slytherin, the Blacks, and Voldemort, murdered by Bellatrix) Potter
Albus (resisted Voldemort's power for fifty years, terminally ill from a Voldemort curse, perished after preparing Harry to defeat Voldemort)
Severus (repented of serving Voldemort, served seventeen years as a triple agent, murdered by Voldemort, but never suspected by Voldemort of being committed to Voldemort's defeat) Potter
Lily (three times foiled Voldemort, honored her husband's sacrifice and refused to give up her baby to Voldemort, murdered by Voldemort) Luna (the only name given to any of Harry's children which did not honor someone deceased before Voldemort's final death, Luna Lovegood was Harry's stalwart ally against Voldemort) Potter
In effect James, Sirius, Albus, Severus, and Lily all lived on through the people named for them because of Harry's and Ginny's love for them. Voldemort, the man who thirsted for immortality, never achieved this.
This I think is Dumbledore's (JKR's also) main point... Life without love is worthless... therefore, Love is worth living for. Love is worth dying for. Love is sacred. Love is Magic.
I think you'll find that Rowlings was just writing a book and didn't have to much underlying thought as to the meaning of Harry's life etc...
My titles for the books would be Harry Potter and the Life, the Heart, the Captive Spirit, the Far-Reaching Struggles, the Life Partnerships, the Identity, and the Love Worth Dying For. (I know I sometimes end sentences with prepositions, sorry.)
I do not know JKR. I do not possess a degree in literature nor writing... nor do I write... I am merely a fan of stories. But when I observe these commonalities, connections, parallels, comparisons, and repetitions in a series, I suspect their inclusion was much more intentional than arbitrary.