Indonesia could well fall apart. West Timor, West Papua, and possibly Bali, as they all have religious and/or ethnic differences with the majority Javans (who dominate the nation). It's not an imminent proposition, though.
In the area, it's vaguely possible that Malaya and Sarawak will split, although it's not too likely in the imminent future.
Kosovo and perhaps Vojvodina may split from Serbia.
The Sudan may fall apart - a southern Christian Sudan, a northern/central Muslim one, and Darfur might become independent or a part of Chad (Janjaweed violence is spreading into Chad, and the Chadians are not happy about it).
Somaliland is basically already independent of Somalia. Puntland may strive for similar recognition.
Iraq might fall apart into 2 or 3 states. Iran is less likely but might have a Kurdish and/or Azeri separatist movement in the northwest. Kurdistan is top on the new nation list.
Chechnya and some of the other south Russian provinces are trying very hard to gain independence, I don't know if they'll achieve it... Russia is trying to keep them just as hard.
Separatist movements amidst the Basques, in Catalonia, Quebec, Puerto Rico, and possibly Brittany or Corsica might succeed.
Northern Italy has an independence movement, they haven't been terribly succesful though.
French Guiana is a definite possibility, although the Guyanas in general are actually among the most likely places to join the US (Guyana in particular has a strong US annexation movement).
Turkey has the Kurds in the southwest and possibly other minorities in the Northwest to deal with.
Georgia has some rebellious provinces that might try a further independence move.
Transdnestria is an issue for Moldova, it may become formally independent or a part of Russia or the Ukraine.
Zimbabwe might do a Somalia in the next few years. Oppressive regime + major economic disruptions due to said regime and AIDS = crazy stuff.