Aside from prestige and possible historical ties, the primary reasons folks are claiming ownership of these uninhabited bits of land has to do with the ability to control sea lanes, defining maritime economic zones, possible tourist dollars in some instance, and oil, rumored to underlie much of the area. The principal islands involved (and the nations claiming ownership) are;
-- Padra Branca Islands, claimed by Malaysia & Singapore.
-- Sipadam & Ligatan Islands, claimed by Malaysia & Indonesia -- this is one that seems most likely to cause trouble in the near term.
-- Louisa Reef, claimed by Malaysia & Brunei.
-- Spratly Islands, claimed by China, Taiwan, Vietnam, Philippines, Malaysia, & Brunei: They're a bunch of some 100 rocks, reefs, cays, shoals, mud banks, and even islands. China claims them all, but occupies only 8, Vietnam has occupied or marked 25, the Philippines 8, Malaysia 6, and Taiwan one.
-- Paracel Islands, claimed by China, which occupies them, Taiwan, & Vietnam.
-- Sabah, claimed by Philippines & Malaysia. This is a province of Malaysia, which the Filipinos claim was ceded to the Sultan of Sulu (now part of the Philippines) back in the 1870s.
In some of these there have also been periodic clashes over who maintains aids to navigation.
The next war may break out because of a dispute over an uninhabited island in Southeast Asia. Border disputes have long been a cause for wars. All it takes is a country that feels it is losing out because a border is not where everyone agrees is should be. Same thing with islands. There are dozens of these island disputes world wide. Most are not active issues, except for the fact that an international treaty (the 1982 Law of the Sea) gives whoever owns these uninhabited rocks rights to fishing, and oil drilling, for over three hundred kilometers from each of these tiny bits of land.