1851 in Wales
- 24 September — Vale of Neath Railway opens from Neath to Aberdare.
- August — William Bulkeley Hughes hosts a banquet at Bangor for Robert Stephenson.
- Richard Fothergill III is prosecuted for running a "truck shop" at Aberdare.
- David Davies (Llandinam) marries Margaret Jones of Llanfair Caereinion.
Arts and literature
- John Blackwell (Alun) — Ceinion Alun (posthumously published)
- Richard Williams Morgan — A Tragedy of Powys Castle
- Thomas Jones (Gogrynwr) — Gweddi Habacuc (cantata)
- John Ambrose Lloyd — Teyrnasoedd y Ddaear (anthem)
- John Owen (Owain Alaw)
- Deborah a Barac (anthem)
- Gweddi Habacuc (cantata)
- 8 February — Sir Marteine Lloyd, 2nd Baronet (d. 1933)
- 10 March — William Haggar, pioneer of the film industry (d. 1925)
- 24 March — Robert Ambrose Jones (Emrys ap Iwan) (d. 1906)
- 15 June — Ernest Howard Griffiths, physicist (d. 1932)
- 8 July — Sir Arthur Evans, archaeologist (d. 1941)
- 12 July — Elizabeth Phillips Hughes, promoter of women's education (died 1925)
- 27 December — Percy Gilchrist, industrialist