Perhaps...
Beatles - I Saw Her Standing There
Mamas & Papas - California Dreamin'
Beach Boys - Sloop John 'B'
Rolling Stones - The Last Time
Monkees - Daydream Believer
Hollies - He Ain't Heavy (He's My Brother)
Gerry & The Pacemakers - Ferry 'Cross the Mersey
Herman's Hermits - I'm Into Somethin' Good
I find those tend to have quite a wide appeal - folkies and non-folkies alike.

As has already been posted, wartime songs - such as the perennial 'Pack Up Your Troubles' and 'It's a Long Way to Tipperary', which you can organise to have one half of the room singing one and the other half singing the other, all at the same time!

Daft things like 'My Bonny Lies Over the Ocean' where people have to stand up on the first word starting with 'B', sit down on the second, and so-on - at the end of the verse, those sitting down got it right! Then you throw in another (fake) verse:

My Bonny is back from the ocean
My Bonny is back from the sea
She brought me a bunch of bananas
For me and my Bonny for tea
(Chorus)

Those still standing at the end got it right this time...