Yokota Fritz wrote to say his "bike route application now works for Singapore. The routing engine is from MapQuest, and cycleway data comes from OpenStreetMap project, so if there are mistakes or shortcomings, users can fix the map info directly and quickly."
Head over to try it out at cyclelicio.us/map and let us know what you think. I gave it a quick look for Holland Village to Changi Village and this is what it spat out; I like the elevantion and biccle relevant directions and timing. Google Maps' bicycle option choked on this.