A visa is generally not needed to transit Singapore - all 3 terminals are connected air-side, and there is no need to go through immigration when connecting between flights.
Further, as a US Citizen, no visa is required even if you want to enter the country - which for a 9 hour layover I would strongly recommend. With that time you could either take one of the free Singapore Tours that run from the airport, or you could simply catch the MRT (train) into the city and spend some time there. The MRT is cheap and easy to catch, and there are plenty of stops near shopping or sightseeing sites that will allow you to make much better use of your time than sitting in an airport!
(On a side note, travelling to Shenzhen via Singapore is a shocking route - it's almost 50% longer than going to Hong Kong and then transferring to Shenzhen - and that's even without considering your 9 hour layover!)