Wif-Fi service is good in Singapore, if a little tightly controlled by the govenment.  But that is good enough for 99% of the visitors.  It becomes inconvenient only if you want to get into extreme websites.  Most public places in Singapore have free wifi, provided by the government together with three wireless operators. Registration is free. Wireless@SG program

However - you can only sign-up online if you have a local (singapore) cell phone number.  Tourists must visit a 'customer service desk' in person at certain branches of SingTel, M1 or iCell and present passport ID for security (same as when purchasing a SIM card).

So you may just find it simpler to use the free hotspots below unless your stay in Singapore is of a longer period:

 Places with free wi-fi that non-locals may also tap on:

1. All McDonalds outlets. (Some of them have powerpoints too!)
2. Gloria Jeans outlets have free internet stations.
3. All Berrylite yogurt stores (e.g. at Novena Square and Parkway Parade). Just approach the counter staff for the password.
4. San Benado on Church St. 
5. All Coffee Bean & Tea Leaf outlets
6. Your hotel/hostel