So we know more about it...
At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: iMac
Model Identifier: iMac7,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 6 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version (system): 1.21f4
Snow Leopard/10.6.x Requirements...
* Mac computer with an Intel processor
* 1GB of memory (I say 4GB at least, more if you can afford it)
* 5GB of available disk space (I say 30GB at least)
* DVD drive for installation
* Some features require a compatible Internet service provider; fees may apply.
* Some features require Apple’s MobileMe service; fees and terms apply.
Which apps work with Mac OS X 10.6?...
Buy Snow Leopard > http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Call Apple Sales...in the US: 1-800-MY-APPLE. Or Support... 1-800-275-2273
I wouldn't upgrade without going to 2 GB, then I may not...
If you need it for iPhone functionality you may have to, but does it work for whjat vyou want now?