There are two contemporary sources: The Croyland Chronicle and Dominic Mancini's Usurpation of Richard III. When these can be checked against other sources, they seem quite reliable. A few London chronicles that are nearly contemporary also exist, and there are some scraps of contemporary sources here and there. The bulk of the source material, however, comes from the Tudor period. Ricardians claim that this taints the sources, as Henry VII's throne was rather shaky and he had every reason to try to strengthen it and to weaken the character and claims of the man he took his throne from.
That's as may be, but the Tudor sources have problems that no one can deny, whatever motives may have caused those problems. The account of the murder of Edward, son of Henry VI, makes a good example. According to the contemporary battle list of the dead, Edward was killed in battle. A contemporary letter confirms this, specifying that George, Duke of Clarence (Richard's older brother) is the man who actually struck Edward down. Enter the Tudor accounts. Now we learn that Edward was captured and brought to the tent of King Edward IV (Richard's and George's older brother). King Edward demands allegiance, and young Edward refuses it, whereupon King Edward slaps young Edward across the face with his gauntlet and says, in effect, "Take him away." Some nobles who have been hanging around fall upon young Edward and slay him. Next account: we learn the names of the nobles. Next account: a nearly verbatim copy of the previous one, with Richard's name tacked on the end of the list. And finally: it was Richard who struck the first blow.
Clearly the Ricardians have a point when they criticise the sources. Indeed, most of the charges levelled at Richard have been dropped, except by such die-hards as Desmond Seward (author of Richard III: England's Black Legend), who clings to this accusation and every other, somewhat to the embarrassment of other traditionalists. The one accusation that shows no signs of being dropped is that of the murder of the eleven and nine year old Princes in the Tower.