During my time living in Singapore I would estimate that 80% of my daily spending was done on credit card, specifically Visa. You can use it in almost all retail and food establishments, public transport, taxi, tourist attractions, etc.
Visa and MasterCard are nearly accepted everywhere. This is to be expected given that Singapore is a leading global financial hub
The next most common card was JCB
American Express for only the most high end places and major tourism businesses like hotels and airlines
The only places that are still primarily cash-based are the food hawker centres and mom and pop restaurants & shops outside of the downtown area. But even the hawker centres are changing, some of them have started accepting EZ Link card recently (it's the metro card used in Singapore, which you can reload at any metro station with your credit card)
My recommendation for travellers is to have a Visa or MasterCard, and keep SGD$100 cash in your wallet. Use ATMs to replenish your cash when you run below $20