There wouldn't be space to list all the tunes , there's literally thousands in the tradition. Here's a few favourites:
Arkansas Traveler

Ashokan Farewell

Athole Highlanders

Banshee

Blackthorne Stick

Blarney Pilgrim

Boys of Bluehill

Calliopie House

Cliffs of Moher

Cock of the North

College Hornpipe (Sailors Hornpipe)

Congress

Cooley's

Cup of tea

Dashing White Sergeant

Dingle Regatta

Donnybrook Fair

Drowsy Maggie

Duke of Perth

Dusty Windowsill

Earl's Chair

Fairy Dance

Farewell To Erin

Flowers of Edinburgh

Golden Keyboard

Gravel Walks

Hag at The Churn

Haste to the Wedding

High Reel

I'll buy boots for Maggie

I wanna be near you

Irish Washerwoman

Jig of Slurs

Keel Row

Kesh

Kid on the Mountain

King of the Fairies

Lark in the Morning

Maggie in the Wood

Maguire & Patterson's

Maid behind the Bar

Margaret's Waltz

Marie's Wedding

Martin Wynn's No 1 & No 2

Mason's Apron

Merry Blacksmith

Miss McLeods

Morrison's

Mountain Road

Musical priest

My Love is but a Lassie yet

My Love is Like a Red Red Rose

Nine Points of Roguery

Off to California

Orange & Blue

Otter's Den

Over the Moor to Maggie

Pinch of Snuff

Planxty Irwin

Rights of Man

Saddle the Pony

Sailor's Bonnet

 Sally Gardens

Scotland the Brave

Sean Ryan's

Si Bheag Si Mhor

Silver Spear

Skye Boat Song

Sligo Maid

Soldiers Joy

Spanish Lady

Spider in the Bog

St Anne's

St Bernard's Waltz

Star of Munster

Statten Island

Swallows Tail

Tam Linn: Tarbolton

Teetotallers

The Rose Tree

Toss the Feathers

Tripping up the Stairs

Trumpet Hornpipe (Captain Pugwash)

Turkey in the Straw

Wise Maid