Originally Posted by MIT_SBM

Sleeping at Changi 'airside' is quite doable and might even be considered nice but I would not recommend sleeping 'landside' at Changi. I have never been able to find an area 'landside' that was quiet enough and dark enough for me to get any comfortable rest. Just to put this in perspective, I can get nice, refreshing sleep in a window coach seat on almost any flight [even in CRJs].

If you have not other choice or just really don't want to go into the city then I would say that you can collect your baggage and stake out any spot you like on the 'landside' and have a go at sleeping. As others have said, I don't think you have too much to worry about regarding theft but I won't go as far as to imply that the risk is zero.