Clones of the Emperor
Palpatine has been shown in several comics to have clones of himself waiting around for his eventual demise. This sounds perfect, since he can transfer his existence into any of them, but how does he explain it to the galactic populus? Does he even try? He has a brand new body, and no doubt feel a few things he hasn't felt in years, such as attraction to someone. This might leave him vulnerable. Plus, I thought that entire story line a little convoluted, so I'm going to say unlikely.
Vader becomes the Dark Lord
Most people claim that Darth Vader is a Dark Lord of the Sith. However, I found a quote in a later novel that has to do with a key aspect of Darth Sidious' power.
Afterwords, Darth Caedus was able to see the future, much like Sidious. Vader is never seen having these abilities, meaning he would be forced to rely solely on his own judgement. While not a bad thing, it would still be difficult for him following in the wake of Sidious. Plus, he would need to train an apprentice of his own from that point.Lumiya to Jacen Solo wrote:"This is the ultimate test of selflessness—whether you're ready to face unending emotional pain, true agony, to gain the power to create peace and order for billions of total strangers. That is the sacrifice. To be vilified by others, by people you know and care for, and for your personal sacrifice to be totally unknown to those billions you save, to do your duty as a Sith. To do your duty for the good of the galaxy."
Mara Jade becomes Empress
Assuming Vader doesn't take the reigns himself, Mara Jade might be a viable candidate. She was the Emperor's Hand, and knew things that even the Grand Admirals didn't know. Whether she would use that knowledge to become Empress or to simply support the next Emperor, however, is unknown. Probably assisting the new Emperor.
A Grand Admiral receives a promotion
The Grand Admirals were the ones tasked by the Emperor and Vader to oversee special military operations, the most well known of course being Thrawn. Thrawn was a skilled manipulator, understanding what makes people think and act. He could easily carve up the Empire or trick people into doing what he wanted, assuming he was even allowed close. As an alien, he might be shunned or even removed from power. I doubt, however, that Thrawn would just go slinking off into the darkness.
A Moff elevates himself above his contemporaries
The Moff council was intended to be a replacement for the Senate, with the Moffs meeting and discussing important events as they served as military governors. Their role seemed to be the day to day government affairs for planets, and thus one would no doubt seek to get himself elected to the role of Emperor. He would face opposition, since like any group of politicians there would be underhanded tactics thrown about, but from a civilian perspective, it would be the most likely.
The Empire collapses into chaos
The entire Empire is a large place. Much too large to be held together by a tiny organization such as the Rebel Alliance. Many of the books talk of the Empire collapsing, mostly due to the chain of command becoming cloudy and confusing. Some admirals become warlords, governors take over as moffs of their own little worlds. The Alliance might one day reunite the galaxy, but it would be much harder since the Rebels would either be working with even less equipment (if they lost at Endor but a few escaped), or they wouldn't have their reputation (if they didn't go to Endor).