Under the Singapore Constitution, presidential approval is
required for the passage of all legislation, after it has cleared
Parliament. Many other important, non-legislative consitutional
powers, in theory, flow from the president. For example, he has the
sole power to appoint judges, and I think he should have the power
to dissolve Parliament as well.
That's the theory, at least. In practice, of course, the situation
is vastly different. As a previous poster pointed out, the
President can only make important appointments of officials on the
recommendation of the Prime Minister - the President can't just
appoint anyone he likes. Also, in practice the Singapore President
has never exercised his power to dissolve Parliament except where
the PM has requested it prior to a general election, nor has he
ever exercised his right to refuse to approve legislation passed by
Parliament. This is in contrast to Presidents in other countries,
who often make full use of their legal authority to check abuses of
power by their respective governments, e.g. in Italy late last
year, where President Ciampi refused to approve a new law that
would have allowed the corrupt PM, Silvio Berlusconi, to protect
the business interests of a media company he owned.