There are a couple of theories on this subject, neither confirmed or denied by Lucas.
The most obvious of these suggests that it was the deflection of his own lightning, originally directed at Mace Windu, which caused Sidious' facial deformity. It is said that the loop caused by Windu's lightsaber explains the enormity of the injuries. However, seeing as Luke suffers a similar attack in Return Of The Jedi, for an even longer period, almost dying as a direct result, other theories have been speculated. It is possible that he was intending to kill Luke slowly and was therefore using less, but still lethal, power, whereas the situation with Mace involved a determined and armed opponent who was an obvious, imminent threat, and Palpatine consequently used more force.
Although he explains to the Senate that he was left "scarred and deformed," there is another theory that Sidious is, at least in some form, a changeling, like Zam Wessel from Episode II, who, by using the dark side, has altered his appearance and disguised his true age to gain popularity in the Senate; a move which has given him his political rank. This theory suggests that the deflected bolts of lightning that burn at Sidious' face do not scar him, but actually rob him of this ability and therefore he reverts to his natural, decayed, gruesome look, seen in this and the later films. Many subscribe to this theory as it seems to fit more within the mythical, and less scientific influences on which Star Wars stories have been based.
Also, in Dark Horse Comics' Dark Empire, The Emperor himself - having transferred his consciousness into a clone body - says "...flesh does not easily support this great power," in explanation to a) how he survived Endor, and b) why he need clones of himself. Granted, most Extended Universe books disregard the Dark Empire series, but it's still approved by Lucas (or his company!) and is - at least officially - canon.
However, especially from the games (Jedi Academy), it can be considered a consequence of a "Dark Rage." In the games, Dark Rage drains your health to make you much stronger. The "health draining" can be considered the deformation of his body. Palpatine was facing a great threat so it is logical that he uses Dark Rage to survive. However, this theory does not explain the deformed appearance. The health draining would not permanently deform the body.
The most likely is the first theory. It is very possible that Palpatine was not expecting Mace to deflect the lightning, so he gave his full power to stop Mace from killing him, thus the full power of the blast hit himself head on with no defense against its force.
Also, it is said the Windu's lightsaber's crystal has properties of both light and dark side. Mace's style of combat, FormVII: Juyo/Vaapad, brings the user dangerously to the dark side, and only the strongest of the Jedi can use this style and not fall to the dark side. It has also been theorized that Palpatine didn't know that a fully formed seventh style existed. So, if Palpatine use a full force lightning attack on Mace, it was amplified even more, and only Sidious' extreme power was able to keep him alive from the deflection.