"Alone Again, Naturally" by Gilbert O'Sullivan. I'd happily sing along to the catchy chorus, vaguely realising it was about someone lonely. I didn't realise that it begins with an intention to commit suicide after being jilted at the altar!
And lesser known, but a very firm favourite of mine was "Promised Land", a Chuck Berry song that was a hit for Johnny Allen. It's all about a lad going west to the "promised land" and ends with him making a reverse-charge phone call saying "Tell the folks back home this is the promised land calling, and the poor boy is on the line!" It always choked me up to think he'd finally made it after such an arduous journey. It was only when we got the internet and I was able to check the lyrics that I found out that the "poor boy" had flown there - not crawled there on his hands and knees! - and, what's more, he'd tucked into a steak on the plane. What?! I still love the song though.