It could run 10.6 as is, but really needs more Memory...
Your iMac can hold 3-4 GB of RAM...
http://www.everymac.com/systems/apple/imac/specs/imac-core-2-duo-2.16-20-inch-sp ecs.html
http://eshop.macsales.com/shop/apple/memory/iMac/Intel_Core_2_Duo_2006
You could run as high as 10.7.5 if Apple still has it available...
Lion/101.7 System requirements
• x86-64 processor (Macs with an Intel Core 2 Duo, Intel Core i3, Intel Core i5, Intel Core i7, or Xeon processor.)
• At least 2GB of memory, I say 6 GB
• Latest version of Mac OS X Snow Leopard (10.6.8), with the Mac App Store installed
• At least 4GB of disk space for downloading, I say 50 GB.
Like Snow Leopard, Lion does not support PowerPC-based Macs (e.g., Power Macs, PowerBooks, iBooks, iMacs (G3-G5), eMacs).
Lion also does not support 32-bit Intel Core Duo or Core Solo based Macs. Rosetta is no longer available in Lion, which means Lion no longer supports PowerPC applications.
http://en.wikipedia.org/wiki/Mac_OS_X_Lion#System_requirements
http://www.apple.com/macosx/how-to-buy/