I've been fixing some articles that link to another article's redirect page (rather than directly to the article) recently (everything linking to "Bein' Green" instead of "It's Not Easy Being Green", for example). It helps Special:MostLinkedPages and other algorithms on the wiki.
Anyway, our article for Kermit's 1979 song started as "The Rainbow Connection" and has never been moved. However, looking at its ASCAP entry and the way it's listed on the original soundtrack release (and I think most subsequent ones), there's no The.
The article title almost certainly should just be "Rainbow Connection", but I wanted to be sure we didn't have any reason keeping the The on there before I moved it and fixed everything on Special:WhatLinksHere.
And now I'm remembering that in Muppets Most Wanted, during the "Interrogation Song", Constantine, posing as Kermit, says "ask who sang "Rainbow Connection"", with no use of "the". Never really thought about it before, and could be chalked up to a dialect difference/not being too familiar with what he's posing as, but it is an example of it being referred to with no "the" when talked about in a sentence.