I'm with the ear worm posters.

Many of us (of a certain age) have a repository of musical memories from varieties of sources. From participation in school shows in the 1950s, I have a whole host of songs from various medleys, such as 'When the red, red robin', 'Shine on, shine on harvest moon', 'Bye, bye, blackbird', 'Moonlight Bay' etc. IMHO these songs have survived because of attractive rhythms, a melodic progression that has a pull on the emotions -- and a straightforward message that is not egocentric!
There were also medleys of British music hall songs ('My old man said "Follow the van"', 'Oh, Mr Porter' etc) and WW1 songs from the trenches.

And from my recent experience of helping a 90 year-old friend (with Alzheimers) into a care home, I was stunned into silence when she voluntarily joined in with an accordionist to sing 'The Northern Lights of Old Aberdeen' -- knowing the words and appreciating the sentiment. (I then found the clip on YouTube of the elderly American man - previously silent in his care facility - who "came to life" when someone played him some blues guitar song -- but apologies for not being able to provide the clicky link!)

But I'd also like to put in a plea for the traditional ballads, given that they deal with universal themes... I know that these songs are considered to be a minority interest, but the fact that they still survive hundreds of year beyond their first recorded collection must mean that they still hold significance for people in the 21st century. (I say this as one of the organisers of a Ballad Workshop in Glasgow which has attracted a good following over the previous three years.)

So, bottom line, my answer is -- give people good melodies with true human emotions and you're on to a winner!