In case anybody is interested in trying to hitchhike in Singapore despite the low cost and great coverage of the public transport, let me share my experience from summer 2013:
There are expressways in Singapore but the distances are so short there are no rest areas along them.
It's not easy to get to an on-ramp for the expressway to Malaysia. Many ramps first go onto another expressway for short distance then split off on the wrong side for hitchhiking. There are also no toll booths (at least I didn't see any).
In any case there's not space for cars to pull over and stop. Even if there's two lanes there's enough traffic that somebody stopping in your lane would be in trouble very soon.
Buses do drive on the expressways it seems so hitchhiking at a busstop may be a possibility - I didn't try it.
It's not legal for a pedestrian to be on an expressway but sometimes footpaths just about lead onto them and the one place lacking signs for things you're not allowed to do in Singapore is at the places you can walk onto an expressway. I never saw any police on the expressway or in fact anywhere in Singapore apart from near the Malaysian border.
Nobody stopped for me on the expressway but if you're younger or less scruffy than me you might have more success.
At a part of the expressway where roadworks were going on a truck driver working there gave me my only lift in the country and dropped me in Sungei Kadut, which is the area just before Woodlands.
If you don't want to risk the tip to walk onto the causeway with the "somebody is picking me up" story, the minimum distance/fare across may be bus 590 from Marsiling MRT station which costs $1.30 currently.
If you need to crash outside there are some parks without fences but with trees in some areas. I hid my tent and had no problem but most of the obvious parks have signs saying "state land", "no trespassing", etc. I'm assuming it wasn't legal in my park either but it had no signs and there were no problems.
Singapore is very safe though there is a slogan you will hear, "Low crime doesn't mean no crime", and neighbourhood watch -style signs on roadsides announcing some crime that occurred in the area in recent months. — Hippietrail (talk) 19:50, 17 August 2013 (CEST)