Hello,
My mid 2007 iMac runs 10.5.8, 10.6.8, 10.75., 10.8.5, & 10.9.0 just fine, depending on what apps you need to run...
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#...
Hardware Overview:
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...
General 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?...
http://snowleopard.wikidot.com/
It's been pulled from the online store & Apple Stores, so you have to call Apple to buy it, last I heard.
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
Other countries...
http://support.apple.com/kb/HE57
It looks like they might still have it...
http://store.apple.com/us/product/MC573Z/A?fnode=MTY1NDAzOA