It’s easy even for an avid theatergoer to become jaded. Years of sitting through sickeningly sweet tales like “Mary Poppins” and obnoxious tourist traps like “Rock of Ages” have done a fine job of demonstrating that musicals, as an art form, can be completely devoid of anything resembling real emotion.

Yet once or twice every season, a show comes around that proves hope is not lost. Among the dancing newsboys and perilously swinging superheroes, it is still possible to find gems of sincerity in today’s musicals.

The original purpose of songs in a play was to convey a character’s feelings and thoughts in a moment of overwhelming emotion when words alone were no longer enough. Many songwriters have given us moments of incredible joy (“I Could Have Danced All Night”), true love (“Some Enchanted Evening”) and overwhelming hopelessness (“I Miss the Mountains”).

Look at “Once,” the 2012 Tony Award-winner based on the movie of the same name. Its familiar plot — boy meets girl, boy falls in love with girl, boy leaves girl — is portrayed in a beautifully simple musical that is really just a sad and bittersweet love story. And if you’re not tearing up by the end, you will find yourself in the minority.

Similarly, “The Last Five Years” began performances off-Broadway at the Second Stage Theater on March 7. Also a love story, it tells the tale of Jamie and Cathy’s failed relationship, which Jamie tells from beginning to end and Cathy recounts in reverse. As the show ends, older Jamie leaves Cathy for the last time at the end of their relationship, while across the stage a younger Cathy sings about all the hope and promise she sees for their future. Admit it — even reading about that makes you emotional.

With shows like these it is impossible to argue that all musicals are devoid of true emotion. Instead, it is shows like “Once” and “The Last Five Years” that prove just how sincere musical theater can be.

— Dylan Jarrett