It is difficult to determine whether Richard II is a tragedy or not. It appears that when Shakespeare first drafted the play he drafted it as a tragedy (and it is one of his earlier plays) however as his folio of plays increased, it fall among his history plays. It should be considered that not all of Shakespeare's plays fall neatly into the categories of tragedy or comedy, and this is particularly the case with his history plays (in particular Henry V).
Richard II is the first play in Shakespeare's history cycle (which begins with Richard II and ends with Richard III, with the King Henry plays coming in the middle). In a sense this history cycle chronicles the fall of the Plantagenat dynasty and the rise of the Tudor dynasty. It should also be noted that the history plays all occur during the period known as the Hundred Years War (which was between England and France), though by the time of Richard III, England had been pretty much kicked out of France, and thus it is interesting to note that upon losing the Hundred Years War, civil war breaks out in England (a war known as the War of the Roses, between the House of Lancaster and the House of York). The losing side in war seems to, in many cases, either collapse into civil war, or undergo a revolution (actually, that is not really the case, but it was in this particular instance).
However, enough of history and on with the play, or the character of Richard II. Richard was the grand son of Edward III (the one who is considered to be the instigator of the Hundred Years War), and was the son of the Black Prince. The Black Prince, being heir to the throne, never actually took the throne as he died before his father (of the black plague, which was ravaging Europe at the time). So, when Edward died, Richard took the throne. However, Richard did not last long as he continued his father's and grand father's wars, but to fight wars, one needs money, so he raised money by confiscating lands and raising taxes. However, his wars never went all that well, and as is the case in such situations, was deposed by the man who would become Henry IV.
The question is whether this play falls into a tragedy. As argued elsewhere I do not see any concept of a tragic flaw in Shakespeare's tragedies, and once again I do not see any tragic flaw in Richard. Yes, he raised taxes, and upset the wrong people, but that is going to happen when one is king. I guess if there was a fatal flaw in Richard it was that he wasn't a particularly strong king. I say that because not only did he get deposed, but because his rival, Henry Bolingbroke, was able to rally support against him. I guess he also wasn't a particularly bright king either as he went to Ireland to fight a war there and pretty much left the kingdom open to Bolingbroke to take it from him. However, I guess that may be the purpose of the history plays, as here we see the end of the Plantagenat dynasty, however the mess that begins with Bolingbroke's usurption will end with the mess that becomes the War of the Roses.
A few other points I wish to raise, and that is that Bolingbroke, when he captures Richard, locks him up. However this isn't in a dungeon or such, but rather in a castle. This is a very luxurious prison, but a prison nonetheless. Further, Richard's death is strangely reminiscent of the death of Thomas Becket. Henry II is said to have cried out 'who will rid me of this troublesome priest' at which point some knights took it upon themselves to kill him, against Henry's wishes. The similar thing occurs here (and it is interesting to note that both incidents involve a Henry). Henry, exacerbated, makes a statement that he does not mean, and assassins that go to Pomfret Castle and slay Richard (though Richard does actually put up a fight - never accuse Shakespeare of being light on the action). However, it appears that this event occurred according to his source, Holingshed. It is also interesting that Richard's assassin is exiled and that Henry mourns over his death. It seems that even though he took his throne, he could not bring himself to kill Richard, for even though he may no longer king in actuality, he is still the king, and to kill him is regicide. Whatever happens to Henry I guess we will see unfold in Henry IV.
By the way I recently watched a Royal Shakespeare Company production of this place, which happens to have David Tennant as the lead role. I have written a post on it (and a more detailed analysis of the play) on my blog.