Houthis and southerners will see Saleh's fall as an opportunity to grab more power and influence, moves that may anger military leaders with a more nationalistic orientation. Demonstrators with a more pro-democratic bent will seek a leader who is not simply Saleh by a different name but someone committed to a more open and accountable political system. Yemeni tribal leaders, always eager to exploit a vacuum, will expand their influence.
Today, much of Yemen is governed at best loosely and at times not at all by the central government, so the further decline of centralized power at the expense of warlords and tribes would not change Yemen overnight. However, it would make Yemen more prone to further regime change and instability, as the alliances and patronage systems Saleh established all come up for grabs.
Saudi Arabia may destabilize things even further. Riyadh views Yemen as the kingdom's backyard and worries that instability there could spread north. Saudi Arabia has often tried, and often failed, to play kingmaker in Yemen. Should a new ruler in Sanaa try to hew an independent line from Riyadh, as Saleh did, the Saudis may give financial and other support to his enemies.
For the United States, the biggest worry is terrorism. Osama Bin Laden could take advantage of additional instability to channel more resources to Yemen. No matter what, AQAP will take advantage of any easing of pressure to plan more attacks and build their organization. A new government, like Saleh's, would probably see AQAP as a relatively minor threat and would focus its intelligence services and political energies on its domestic enemies and rivals, leaving counterterrorism a distant second. There is only so much cooperation the United States can buy.
U.S. influence in Yemen is quite limited. The United States can try, like Saudi Arabia does, to support its favored local factions against their rivals. This may put Washington crossways with Riyadh if we have different favorites. An even bigger problem is that the United States lacks the intelligence for such deft dancing and would likely be manipulated by local players.
So, as it always does, Yemen will go its own way while the world averts its gaze. Unfortunately for both Yemenis and the United States, Yemen's future may be worse than its present.