The Scots Musical Museum version, which Burns contributed, is not in the DT. This is the one in James Kinsley's Burns: Poems and Songs (Oxford, 1969, p, 353). Copied from a reprinted edition of The Scots Musical Museum (four-volume edition, 1853; Folklore Associates, 1962, p. 426; with the original tune).
Auld lang syne.
Should auld acquaintance be forgot And never brought to mind? Should auld acquaintance be forgot, And auld lang syne!
Chorus: For auld lang syne my jo, For auld lang syne, We'll tak a *cup o' kindness yet for auld lang syne.
And surely ye'll be your pint-stowp! And surely I'll be mine! And we'll tak a cup o' kindness yet, For auld lang syne. For auld, &c.
We twa hae run about the braes, And pou'd the gowans fine; But we've wandered monie a weary fit, Sin auld lang syne. For auld, &c.
We twa hae paidl'd in the burn, Frae morning sun till dine; But seas between us braid hae roar'd Sin auld lang syne. For auld, &c.
And there's a hand, my trusty fiere! And gie's a hand o' thine, And we'll tak a right guid-willie-waught, For auld lang syne. For auld, &c.
*Some Sing, Kiss, in place of Cup. [--original note]
Ronnie Brown sings this version on The Complete Songs of Robert Burns, volume 3 (Linn Records CKD 062) [also on Auld Lang Syne: A fine slection of popular Robert Burns songs (Linn Records CKD 088)]. Rod Paterson's singing (also with the original tune) is based on this, but the order of subsequent verses are changed (on Celtic Collections, vol. 2: Songs of Robert Burns (CDGMP 8002). I have heard Jean Redpath's recording.
The first setting with the now well-known tune [that of "O Can Ye Labor Lea"] is in George Thomson's Select Collection of Original Scot[t]ish Airs (1779) [photo of the page is in James J. Fuld, The Book of World-Famous Music, plate I], under the title of "Should auld acquaintence be forgot," whose setting is by Czech composer Leopold Kozeluch. The Kozeluch version was a two-part song, which was "simplified." His original setting (1798) was a four-part song with violin, cello, and piano accompaniments, and is on Scottish Early Music Consort's Burns: Songs & Music (Chandos CHAN 8636) [= Auld Scottish Sangs: Scots songs collected by Robert Burns (Chaconne/Chandos CHAN 0581)].
George Thomson asked Beethoven to provide an arrangement, which is on Complete Beethoven Edition, vol.17 [Volkslied-Bearbeitungen] (Deutsche Grammophon 453 786-2) [Felicity Lott (soprano), John Mark Ainsley (tenor), Thomas Allen (bariton)] and on The New York Vocal Arts Ensemble, Beethoven Folk Song Arrangements for Vocal Ensemble (Arabesque Z6672).
There're hundreds of recordings (search Amazon, Yahoo, CD NOW, CD Universe, Barnes & Noble). Some interesting recordings (at least to me) are on these CDs: Dame Nellie Melba (Larrikin CDLRH221) [recorded 1905]; V.A., The Star o' Rabbie Burns (Moidart Music Group MIDCD 004) [sung by Peter Dawson (recorded 1930)]; Royal Scottish National Orchestra Chorus and Moira Anderson (soprano), Songs of Scotland (ASV CD WHL 2087); V.A., Songs of Scotland: A Celebration of the Magic of Scotland (Music Digital CD 6062) [John Laurie (reading) / The Regimental Band of the Grenadier Guards with Guest Pipers]; V.A., New Orleans Brass Bands: Down Yonder (Rounder CD 11562) [Dejan's Olympia Brass Band]; V.A., Alligator Stomp, vol.4: Cajun Christmas (Rhino R2 71058) [Michael Doucet (fiddle) and others].