Here are some local apps that you may find useful:
1. iSinGeo is a web app that allows you to find out what's close to a location that you specify. Input a road name, a bus stop number (they have numbers? who knew?), an MRT station, a hotel or a shopping mall. It locates nearby cinemas, ATMs, restaurants, bars, Apple shops, bicycle shops, Starbucks outlets and much much more. Very cool app that is based on the excellent SinGeo website.
2. Cinepura is a web app that gives you movie screening times. Very handy when you arrive at the Golden Village cineplex at VivoCity only to find that tickets for Wall.E have sold out and you need to find another cinema that shows it in the next hour or so.
3. Transit and MRTSchedule are iPhone apps for jailbroken iPhones. They look very useful and the developer appears to be planning to convert these apps to work for normal iPhones. Transit is a journey planner that tells you how to get from point A to point B by bus. It appears to be like Iris. MRTSchedule tells you when the first and last train leaves from the different stations.
If I've missed out anything, let me know and I'll update the list.