This is from my copy of A Handbook of English Heraldry (11th edition, published 1914) by Charles Boutell: “a concise list of the more important of the Badges that have been borne by the Sovereigns and Princes of England”.

William Rufus: A Flower of five foils.
Henry I.: A Flower of eight foils.
Stephen: A Flower of seven foils: a Sagittarius.
Henry II.: The Planta-genista: an Escarbuncle: a Sword and Olive-Branch.
Richard I.: A Star of thirteen rays and a Crescent: a Star issuing from a Crescent: a Mailed Arm grasping a broken Lance, with the Motto—”Christo Duce.”
John and Henry III: A Star issuing from a Crescent.
Edward I.: An heraldic Rose or, stalked ppr.
Edward II.: A Castle of Castile
Edward III.: A Fleur de Lys: a Sword: a Falcon: a Gryphon: the Stock of a Tree: Rays issuing from a Cloud.
Richard II.: A White Hart lodged: the Stock of a Tree: A White Falcon: the Sun in splendour: the Sun clouded
Henry IV.: The Cypher SS: a crowned Eagle: an Eagle displayed: a White Swan: A Red Rose: a Columbine Flower: A Fox’s Tail: a crowned Panther: the Stock of a Tree: a Crescent. His Queen, Joan of Navarre: An Ermine, or Gennet.
Henry V.: A Fire-beacon: a White Swan gorged and chained: a chained Antelope
Henry VI.: Two Ostrich Feathers in Saltire: a chained Antelope: a Panther
Edward IV.: A White Rose en Soleil: a White Wolf and White Lion: a White Hart: a Black Dragon and Black Bull: a Falcon and Fetter-lock: the Sun in splendour
Henry VII.: A Rose of York and Lancaster, a Portcullis and a Fleur de lys, all of them crowned: a Red Dragon: a White Greyhound: a Hawthorn Bush and Crown, with the cypher H.R.
Henry VIII.: The same, without the Hawthorn Bush, and with a White Cock His Queens: Catherine of Aragon—A Rose, Pomegranate, and Sheaf of Arrows. Anne Boleyn—A Crowned Falcon, holding a Sceptre. Jane Seymour—A Phoenix rising from a Castle, between Two Tudor Roses. Catherine Parr—A Maiden’s Head crowned, rising from a large Tudor Rose.
Edward VI.: A Tudor Rose: the Sun in Splendour.
Mary: A Tudor Rose impaling a Pomegranate— also impaling a Sheaf of Arrows, ensigned with a Crown, and surrounded with rays: a Pomegranate.
Elizabeth: A Tudor Rose with the motto, “Rosa sine Spinâ” (a Rose without a Thorn): a Crowned Falcon and Sceptre. She used as her own motto—”Semper Eadem” (Always the same).
James I.: A Thistle: a Thistle and Rose dimidated and crowned,. No. 308, with the motto—”Beati Pacifici” (Blessed are the peacemakers).
Charles I., Charles II., James II.: The same badge as James I., without his motto.
Anne: A Rose-branch and a Thistle growing from on branch

Some notes on the list:

  • Or (when in italics) is the heraldic term for gold rather than the conjunction, so a Rose or, stalked ppr is a golden rose with a purple stalk (ppr is shorthard for purpure)
  • The Planta-genista of Henry II is the broom, and gives the Plantagenets their name. An Escarbuncle is like an eight-spoked cross (it looks a bit like a cartwheel without the wheel)
  • Plenty of pub names: White Hart, Sun in Splendour, Spread Eagle (an Eagle Displayed), Red Dragon
  • Impaled and dimidated both mean that the badge is split into two halves with one image on each side. When impaled each half shows the full badge scaled to fit the space; then dimidated the image is cropped, as if two complete badges were taken, sliced in two then stuck together. This can lead to some pretty funny arms (looking at you Prochowice).
  • Even if your Tudor history is rusty you should be able to figure out which of Henry’s wives bore which of his children.
  • A Badge is similar to, but distinct from a Coat of Arms or a Crest. Generally a Badge resembles a single charge and may be borne by itself (Arms must appear on a shield or lozenge, a Crest on a coronet). A good local example would be the Bear and Ragged Staff of the Beauchamps and Nevilles