1. Joan, by a mistress named Clemence (politely called "regina Clemencie" by the Tewkesbury Annals). She married Llywelyn Fawr in 1206 and they had several children. Legitimated by a decree of Pope Honorius II in 1226 (Rex anglie solutus te genuerit de soluta, "King John, when unmarried, fathered you by a maiden woman") She died April 1236.
2. Richard, called "de Warenne" because his mother was the sister of William de Warenne, Earl of Surrey (and the daughter of Hamelin, and thus John's first cousin), fl. 1214. He married Rohese of Dover and became Baron of Chilham. They had several children.
3. Oliver, by a mistress named Hawise, fl. 1216 while defending Wolvesey Castle for the Bishop of Winchester. The next year he was granted the lands formerly held by Peter Fitz Herbert. In 1218 he joined the papal legate Pelayo and left for Damietta, and never returned. Based on the fact he was active in warfare by 1216, he may have been born c. 1190.
4. John, a clerk in London, fl. 1201.
5. Geoffrey, fl. 1204, died in 1205 while on expedition in Poitou.
6. Henry, knight, sent as a student to the Prior of Kenilworth in 1207. Participated in the expedition to Poitou in 1214. This is the same Henry who John referred to as "Henry, who says he is my son but who is truly my nephew". He was granted lands in Cornwall and Lincoln. He married an heiress, Eve de Blanchminster but they had no children. He died in early April 1245.
7. Osbert, knight, fl. 1215. He received lands in Oxfordshire, Suffolk, Essex, and Sussex. He died in 1248.
8. Eudes, fl. 1233, granted lands in Hertford and Essex. He seems to have been associated with his half-brother Richard of Cornwall, witnessing charters for him and joining him on Crusade in 1240. He died in the Holy Land in 1241.
9. Bartholomew, clerk, member of the order of Friars Preachers, fl. 1252.
10. Maude, abbess of Barking, fl. 1247 (not to be confused with her aunt Matilda, an illegitimate daughter of Henry II who was also abbess of Barking). She died in Jan/Feb 1252.
11. Isabel, married Richard Fitz Ives, lord of Degembris in Cornwall. They had two sons, William and Richard, and a daughter Isabel.
12. Philip, fl. 1263. Granted lands in Surrey, married a woman named Lavinia and they had at least one son, Henry.
King John seems to have been having illegitimate children over an extended period of time, both before and after becoming king. He also seems to have had a stable of mistresses, although unfortunately we rarely know which woman was the mother of which children. A woman named Suzanne appears as domicella, amica domini Regis (lady-in-waiting and lover of the king) in one source. Richard's mother was John's own first cousin, the daughter of Hamelin, himself the illegitimate son of Geoffrey of Anjou (see the Chronicle of Richard of Gloucester). His mother was one of the most high-ranking of John's mistresses, and he is sometimes called by her name, as in 1233 when he is referred to as Ricardum de Warenne, filium Regis Johannis in a record of the Bishop of Lincoln. Another high-born mistress was Hawise, countess of Aumale. There's an odd 1209 entry in the Pipe Rolls where Peter des Roches sends John a barrel of wine in apology for Roches forgetting to give Hawise a belt John had sent her. John was certainly generous enough in forgiving the debts of Hawise's son, William de Forz.
Bizarrely, the The Plantagenet Connection journal makes Joan's mother Constance of Brittany, the widow of John's brother Geoffrey, which is unlikely to say the least! Joan's mother was probably Clemence, daughter of Roger de Dauntsey of Wiltshire, and wife of Nicholas de Verdun. In 1228, Clemence and her husband were granted custody of Susanna, Joan and Llywelyn's daughter, who was then being held hostage in England.
I'm fascinated by the case of Henry, "who says he is my son but who is truly my nephew". He was probably born sometime in the 1190s, and probably earlier than 1200. This would preclude him being a son of Young Henry (died 1183) or Geoffrey (died 1186). So it seems he would be the son of either Richard or John, unless he's older than I think.