This list is limited to text composed by Tolkien in Old English which are at least several lines long, ignoring smaller things like single lines of dialogue, names, and Old English titles Tolkien gives to his non Old English works
Many of these texts do not have titles given by Tolkien, and so I refer to them by the opening words instead.
All together, there is a little over 1,000 published lines of Tolkien's Old English compositions, the vast majority of which (around 70%) are not accompanied by any Modern English translations.
There are likely more that remain unpublished.
Legendarium related
Ælfwine's translations In parallel with 1930s Silmarillion texts, Tolkien also tried writing some of them as prose in Old English. These have been published in The Shaping of Middle-earth, all without translation. (Some excerpts with translation and analysis can be found in "Writing for an Anglo-Saxon Audience in the Twentieth Century: J.R.R. Tolkien's Old English Chronicles" by Maria Artamonova)
- Pennas - (translation by Ælfwine of the first four paragraphs of Quenta Noldorinwa) - Shaping, 56 lines
- 'Þéos gesegen wearþ ǽrest...' (translation by Ælfwine of the opening of the Annals of Valinor, until just after the destruction of the two trees) - Exists in two versions, of 55 lines and 158 lines. Christopher says that the second is very close to the Modern English version given in the book. Two other very short texts (27 lines and 10 lines) are also given, further developing the opening lines of the second version.
- Beleriandes Géargesægen (translation by Ælfwine of the opening of the Annals of Beleriand, until just after the Dagor Aglareb) - 88 lines
The Lost Road / The Notion Club Papers Both incarnations of Tolkien's unfinished time travel story featured a number of pieces in Old English, most accompanied by translations. They can be found in The Lost Road and Other Writings and Sauron Defeated.
- 'Thus cwæth Ælfwine Wídlást...' (Ælfwine's words before departing on his last voyage, included in his preamble to the Silmarillion, and heard in dream by Alboin Errol in The Lost Road and by Edwin Lowdham in The Notion Club Papers) - Lost Road (3 versions) and Sauron Defeated (1 version), one line of prose and five lines of verse, all four versions include a translation. The verse portion of three of the four versions together with their translations are reproduced in Collected Poems #74G.
- 'Hwæt! Éadweard cyning Ælfredes sunu...' (verse prepared by Ælfwine to sing to King Edward) - Sauron Defeated, four lines of verse, with translation. This episode is also prefaced by four lines of Old English dialogue with translation between Ælfwine and the King.
- 'Monað modes lust mid mereflode...' (verse actually sung by Ælfwine for King Edward, similar to The Seafarer. Also heard in dream by Lowdham.) - Lost Road (1 version) and Sauron Defeated (two versions), seven lines of verse, two of the versions include a translation. Those two versions together with their translations are reproduced as Collected Poems #144.
- 'Hi alle sǽ on weorulde oferliodon...' (Lowdham's manuscript of the Fall of Numenor) - Sauron Defeated, 36 lines of prose, with translation. Also an earlier 43 line version, with translation, and two related fragments of 15 and 7 lines, only the first of which has a translation.
- 'Hwæt! Wé on geárdagum of Gársecge...' (verse about King Sheave sung by Tréowine)- Sauron Defeated, six lines of verse, not translated, but accompanied by a modern english version that seems fairly close.
Rohan The language of Rohan is rendered in the books as Old English. Most of this is limited to names and the occasional isolated line of dialogue, but there is one longer segment in an earlier draft published in The Treason of Isengard.
- 'Abídað cuman uncúðe!...' (challenge that the Rohirrim guards give to Aragorn and Legolas when they arrive at Edoras, similar to a passage of Beowulf) - six lines of dialogue with translation
Non legendarium related
Almost all of these are poems, many of which have only been published in very obscure places.
For some analyses on the poetry, see "Poems by Tolkien in Other Languages", by Tom Shippey, in J.R.R. Tolkien Encyclopedia: Scholarship and Critical Assessment.
Tribute poems
'Úþwitа sсеаl eаldgesægеnum...' - thirteen lines of verse in obituary for Henry Bradley, published in Bulletin of the Modern Humanities Research Association (1923), not translated. Currently in the public domain in the US. Reproduced as Collected Poems #72.
úþwitа sсеаl eаldgesægеnum
fród fуrngewritum féоlan gеorne,
hár оnd hygegléaw hord sсéawian
wordа оnd rеorda, widе geоnd eоrþan
snyttrо séсan, sméaþоncol mоn;
wísdóme þéon, wunian on áre,
rúnа rǽdаn, rinсas lærаn,
оþþæt sсír mеtod to gеsceаp-hwílе
hinе ellоr aсiegþ eаrd geséсan.
Þа felаléof férеþ on fréаn wǽrе,
wеrum bewópеn wоruldfréоndum,
léоdwitа líþоst ond lárgeornоst,
démena gеdéfеst оnd déорhýdgоst.
Bummsdrápa - "a satirical poem, referring to the Kolbítar", University of Leeds archive, currently unpublished
Brýdleop - 91 lines of verse followed by 3 lines of prose, written as a song for the wedding of E.V. Gordon and Ida Pickles in 1930. Published as Collected Poems #120, together with a Modern English translation from Arden Smith.
For W.H.A. - twenty-seven lines of verse written about Wystan Hugh Auden, modeled after the Old English poem, "The Gifts of Men", published with translation in Shenandoah: The Washington and Lee University Review (Winter 1967 issue), and reproduced as Collected Poems #195.
'Hwaet! we Inclinga...' - four line verse fragment about the Inklings, published with translation in The Inklings (1979), reprinted a few other places.
Songs for the Philologists Tolkien contributed six Old English poems to the 1936 collection Songs for the Philologists, all without translation, but usually with an indicator of the tune. Three of these have been reprinted with translation by Tom Shippey in the The Road to Middle-earth. All six have been reprinted with alternate manuscript variations and translations by Wayne Hammond and Christina Scull in Collected Poems.
- Syx Mynet - twenty-eight lines of verse translating the nursery rhyme "I Love Sixpence", reprinted with translation ("Six Coins") as Collected Poems #97.
- Ruddoc Hana - forty-eight lines of verse translating the nursery rhyme "Who Killed Cock Robin?", reprinted with translation ("Robin Cock") as Collected Poems #77.
- Ides Ælfscýne - thirty-seven lines of verse about a lover being abandoned by his elf-mistress, to the tune of "Daddy Neptune", reprinted with translation ("Elf-fair Lady") in The Road to Middle-earth, and as Collected Poems #78.
- Éadig Béo Þu! - twenty-four lines of verse about the language vs literature rivalry, to the tune of "Twinkle, Twinkle, Little Star", reprinted with translation ("Good Luck to You") in The Road to Middle-earth, and as Collected Poems #80.
- Ofer Wídne Gársecg - twenty-six lines of verse similar to and to the tune of "The Mermaid", reprinted with translation ("Across the Broad Ocean") in The Road to Middle-earth, and as Collected Poems #81.
- La, Huru - fifteen lines of drinking song verse to the tune of "O'Reilly", reprinted with translation ("Oh Truly") as Collected Poems #98.
Others
Enigmata Saxonica Nuper Inventa Duo - sixteen lines of verse containing two riddles (Spoiler: "egg" and "candle"), published in A Northern Venture (1923), not translated. Reprinted with a translation for the second riddle in The Annotated Hobbit (2002). Bother reprinted with a translation as Collected Poems #71. Currently in the public domain in the US.
I.
MEOLCHWITUM sind marmanstane
wagas mine wundrum frætwede:
is hrægl ahongen hnesce on-innan,
seolce gelicost; siththan on-middan
is wylla geworht, waeter glaes-hluttor;
Thær glisnath gold-hladen on gytestreamum
æppla scienost. Infær nænig
nah min burg-fæsten: berstath hwæthre
thriste theofas on thrythærn min,
ond thæt sinc reafiath – saga hwæt ic hatte!
II.
Hæfth Hild Hunecan hwite tunecan,
ond swa read rose hæfth rudige nose;
the leng heo bideth, the læss heo wrideth;
hire tearas hate on tan blate
biernende dreosath ond bearhtme freosath;
hwæt heo sie saga, searothancla maga.
'Ætla Guðhere ar onsende...' - forty lines of verse corresponding to the first eight stanzas of the Old Norse "Atlakviða", published with translation in The Legend of Sigurd and Gudrún (2009)
'Þa hlog Hagena þe man heortan scear...' - twenty-eight lines of verse corresponding to the stanzas 24-32 of the Old Norse "Atlakviða", published with translation in The Legend of Sigurd and Gudrún (2009)
'On ǽrdagum wæs wuniende...' - 212 lines of prose translating Tolkien's "Sellic Spell", published in Beowulf: A Translation and Commentary (2014), not translated.
'Þa Mónan Cyning to Moldan Ság' - An Old English verse translation of "The Man in the Moon Came Down Too Soon", abandoned after two lines. Published in Collected Poems #24D.
'On þisre béc scop hafaþ...' - Three lines of prose written above a list of Tolkien's poems. Printed with a rough translation in Collected Poems Appendix III.
Bealuwérig - 28 lines of verse corresponding to Jabberwocky by Lewis Carroll. Published as Collected Poems Appendix V, together with a translation by Arden Smith.