Real lyrics, to serious songs, which make me want to chuckle or smirk:

"Havin' My Baby" -- Paul Anka -- the whole song

Any song where the guy sings something about "...where my love lies waiting... ."   (E.g., Paul Simon's "Homeward Bound," Dan Fogelberg's "High Mountain Snows.)  I always picture some poor woman bedridden for years, waiting for her love to return -- or maybe a real couch-potato mama lying in bed eating bon bons and watching soap operas until her man returns.

Neil Diamond again:  "...Songs she sang to me, songs she brang to me... ."  (Play Me)

Frankie Valli -- "Rag Doll "...such a pretty face should be dressed in lace"  -- I always picture one of those old fashioned hat lace veils that hid most of the face -- or maybe a woman with bits of lace pasted all over her cheeks.

Marion, I agree that "...around the bloomin' heather..."  always sounds like mild cursing to me and, "Will ye go, Lassie, go?" always makes me think of the parody where the owner is trying to get the collie to "go" so he can take her home.

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Songs/lines that crack me up because I have screwed up the lyrics in the past, because I've heard others screw them up, or because they so strongly suggest a parody include:

Autumn Leaves:  "I see your lips, the summer kisses... ."  When I sing "I see your lips, " I always have the urge to add, "...and I'll raise you... ."

Snowbird.   It's so hard not to sing, "Spread your f***ing wings and fly away... ."

Trees, They Grow High -- I so badly want to sing "...his young butt is daily growing... ."
 

Massa's In De Cold, Cold Ground  -- Not that I would sing this, anyway, but when I hear even the title, I always think of that well-known blooper someone once made in introducing the song as "M' ass Is In De Cold, Cold Ground."

Let Us Break Bread Together On Our Knees-- At least half the time, I start to sing, "When I fall on my face, with my..." before I remember that it is "...fall on my knees with my face to the rising sun."
 

Winter Wonderland --  ever since my mondegreen-prone cousin sang "Later on, we'll perspire as we sit by the fire... ."
 

Tiptoe Thru The Tulips  -- How can you not think of Tiny Tim?
 

Hey, Good Lookin' -- ever since I slipped and sang "How's about keeping somethin' up for me?"

And, finally, "Are You Lonesome Tonight?" -- ever since I heard the Elvis (live at Las Vegas) recording where he sang, "Do the chairs in your parlor seem empty and bare.  Do you gaze at your bald head and wish you had hair?"  (a spontaneous reaction to seeing two bald men sitting in the audience).