How do you think the reigns of Robert and Joffrey will be remembered by history? Will they be known as a drunken whoring do-nothing king who usurped the rightful monarch and a stupid vicious sadist who plunged the realm into civil war, or a great warrior king who saved the realm from the depredations of the Mad King and brought a decade and a half of piece and the noble boy king who defended Kings Landing from his demon worshipping uncle only to be murdered by his other uncle, the evil Imp?

Well, we can see from WOIAF how Robert is viewed:

Since the fall of House Targaryen, the realm has prospered greatly. Robert, the First of His Name, took charge of a fractured Westeros and swiftly healed it of the many ills inflicted by the Mad King and his son. As his first act, the unwed king took to wife the most beautiful woman in the realm, Cersei of House Lannister—thereby granting to House Lannister all the honors that Aerys had denied it. And though all know Lord Tywin might well have become Hand again, the king, in his graciousness, gave that office to his old friend and protector, Lord Jon Arryn, instead. The wise and just Lord Arryn has indeed helped the king shepherd the realm to prosperity since.

But this is not to say that Robert’s reign has been completely untroubled. Six years after he was crowned, Balon Greyjoy unlawfully rose against his king—not for any harm done to him or to his people but merely out of wanton ambition. Lord Stannis Baratheon, Robert’s middle brother, led the royal fleet against Lord Greyjoy, while King Robert himself rode at the head of a mighty host. Great feats of arms were performed by King Robert when Pyke was eventually taken and subdued. The king then made Balon Greyjoy—the pretender to the crown of the Iron Isles—bend the knee to the Iron Throne. And as assurance of his fealty, his only surviving son was taken hostage.

Now the realm is at peace, and all that Robert’s ascension to the throne once promised has come to pass. Our noble king has overseen one of the longest summers in many years, filled with prosperity and good harvests. Moreover, the king and his beloved queen have given the realm three golden heirs to ensure that House Baratheon will long reign supreme. And though a false King-beyond-the-Wall has recently declared himself, Mance Rayder is an oathbreaker fled from the Night’s Watch, and the Night’s Watch has always brought swift justice to those who have betrayed it. This king will amount to nothing, as have all the other wildling kings before him.

As for Joffrey, I think it depends on who wins the War of Five Kings.