Currently I have dozens of favorites, but three of the top would be Ashoken Farewell, Elk River Blues, and Sandy River Belle.

Pretty Saro is definitely one of them when I first heard Iris Dement sing it

For me, it actually changes as I learn new songs. I have so many. Currently, I'd say:

My Heart Will Go On (the Titanic song)

Goodbye is Not Forever (Bing Futch)

This Old Guitar (John Denver)

Three???!!! Who can only have three! Well, a few of my favorite ballads are:

Rothesay Bay, Ca' The Yowes, Caller O'u, The Gairdner And The Plooman, The False Lover Won Back, The Maid Gaed To The Mill, Maggie Lauder, The Golden Skein, Today, Believe Me If All Those Endearing Young Charms, Lass From The Low Countree

Glendy Burke

Hard Times Come Again No More. both by Stephen Foster

Grandfather's Clock.

I prefer Hal-an Tow as a group a capella "chant" rather than an accompanied tune.  What would be perfect is to do this one with my Anglo-Saxon Lyre.

So far? 

"Hal an Tow" (Watersons version)
"Hard Times Come Again no More"
"Shenandoah"

My top 3 are:

When I Survey the Wondrous Cross (same tune as “the waters wide” and the other traditional one)

Jesus, Lover of My Soul (by Paul Oakley)

Hark the Herald Angels Sing (cant play this one satisfactorily yet...)

Here's a link to the sheet music for The Ludlows - it is in D, so it would be very easy to tab, at least the melody line.   https://www.sheetmusicdirect.com/en-US/se/ID_No/111153/Product.aspx

OH that's hard.  Too many!  Right now I really do love A Man's a Man for A' That though....

I probably have about three hundred favorites! Yet I'll name three here.  :)

And Can It Be - Charles Wesley

Peace Train - Cat Stevens (Yusuf Islam)

Hard Times Come Again No More - Stephen Foster

James Horner's The Ludlows from Legend of the Fall

I wish I could find a way to tab this song. 

Hmmm....dulcimer tabbed songs, Going Home, Somewhere over the rainbow, Summertime

Favorites?  Depends on my mood.

I will say that I think the two most beautiful melodies ever written are Danny Boy (Londonderry Air) and Greensleeves.

Three that have some meaning for me:

There's A Meeting Here Tonight sung by the Limeliters

Jimmy Newman written and sung by Tom Paxton

Paradise written and sung by John Prine

My three favorite hymns:

A Mighty Fortress Is Our God

Now Thank We All Our God

My Life Flows On In Endless Song

I could make up lots of categories for three songs, but I'll stop with those two.

Ken

"The dulcimer sings a sweet song."

I'll stick to my three favorite old ballads, all of which sound great either fingerdance-drone or noter-drone style:

Lord Lovel (Frank Proffitt Version)

Barbara Allen (Sheila Kay Adams Version)

Pretty Saro (Gillian Welch Version)

Or maybe my three favorite hymns:

Amazing Grace

Farther Along

Long Time Traveling

Or should I stick with my three favorite folk-rock songs, none of which I play on the mountain dulcimer:

Eve of Destruction (Barry McGuire)

Suite Judy Blue Eyes (Stephen Stills)

After the Gold Rush (Neil Young)

Or maybe my three favorite uilleann pipe tunes:

Lark in the Morning (Seamus Ennis)

The Gold Ring (Liam O'Flynn)

The Kesh Jig (Paddy Keenan)

I'm sorry I couldn't help myself, but the first three songs listed are my favorites on the mountain dulcimer.

Only 3???

Lay The Bend To The Bonnie Broom -- an early version of Child Ballad #1 Riddles Wisely Expounded, which we know as The Riddle Song

Massacre At Glencoe -- Scottish 'dirge'. "Cruel is the snow that sweeps Glencoe and cover the grave of o' Donald..."

Hughie The Graeme -- Scottish Border Ballad which mentions my clan Hume

Three "moderns":

Don't Let Us Get Sick by Warren Zevon, the theme song for those of us over 60

Last Farewell by Roger Whittaker, in the great ballad tradition

Suzanne by Leonard Cohen

Three of my favorites are:

     The Parting Glass (traditional Irish)

     Song of the Chanter (not technically a song, because there are no words as far as I know)

     Jet Plane (contemporary, John Denver)

And yours?