Especially when a song is written for a soundtrack, but sometimes just 'cause, an amazing song with have an odd title. The kind of title that, if they thought they had a hit song, would never be the title, or that, if you were humming it to yourself, singing the refrain, you'd have the title on the tip of your tongue. Sometimes it's worth it, sometimes it's pr'y cutting into the viability of the song, commercially or in terms of play.
Motel Sex, off the Vampires soundtrack, is composed by John Carpenter and features Jeff Baxter, Steve Cropper, and other top flight badass talent and it sounds awesome.
Yasushi Ishii's Severe Gun Fight at the Hill of Casualties from the Hellsing soundtrack, similarly, is great. Sweet groove. But, you know, it's a very evocative but not at all punchy title.
I Only Wanted a Buddy, Not a Sweetheart. It's the opening lines. It's sensible. It's comprehensive. It's too long for a DJ to bother with.
The only time I've ever heard a radio station play it, they couldn't be bothered to say all of Hum Allah Hum Allah Hum Allah. And, again, that's not faulting either the title or the DJ. I could ask "Why would you?" and come up with some good reasons to use the whole name, but simultaneously, I accept that it's not only easier, it is often preferable to just shorten it and go "Hum Allah."
Panic! At The Disco... yes, admittedly something of a guilty pleasure for me, and in their heyday were considered a more theatrical version of labelmates Fall Out Boy, but I remember their first 2 hits called "I Write Sins, Not Tragedies" and "But It's Better If You Do". The song titles on their debut album were taken from movies, books, and the like. I thought it was kind of novel amid the ocean of song titles that are taken from songs' choruses, but there's still something of an awkwardness about it.
Also, Portishead, on their album Dummy. Their best known songs off Dummy are "Glory Box" and "Sour Times". You'd expect those songs to have titles like "To Be A Woman" and "Nobody Loves Me" respectively. Especially when you don't know what a glory box is, the title can elicit some confusion. Awesome songs both, though.
Guided by Voices' Robert Pollard is kinda the king at this. I remember a friend of mine who wasn't familiar with them really loved one of their songs and hummed it for me. You should have seen his face when I told him it was called "Tractor Rape Chain".