Citizens of many nations are able to enter Singapore for up to 30 days visa-free -- so there's no need to get a visa in most cases -- and 30 days is more than enough to see all the sights you could possibly imagine in Singapore.
Some nationalities, including the following: Afghanistan, Algeria, Bangladesh, Egypt, India, Iran, the Central Asian states and Russia, Iraq, Jordan, Lebanon, Libya, Morocco, Myanmar, China, Pakistan, Saudi Arabia, Somalia, Sudan, Syria, Tunisia and Yemen are required to get a visa to enter Singapore.
From the Travelfish blogs
How to extend your Singapore visa online
Stays may be extended online via the e-XTEND service.
All tourist entries are single entry only. The arrival and departure stamps are small, quarter page ones.
Overstaying your visa in Singapore is not encouraged -- especially as you can extend your stay via the service mentioned. At a minimum an overstay attracts a fee of $30.