I am just wondering if it's possible to stack Cisco 3750 switches using their ethernet interfaces? I don't have the proprietary stacking cables.
Unfortunately, you'll need the StackWise cables to stack 3750's. (And the StackWise modules as well depending on your switches.)
See this Cisco white paper on Cisco StackWise for more information.
Like @Brett said, StackWise is not possible without the use of stack ports.
However, there is also really really old Cisco switch feature called cluster which uses just ethernet ports.
I personally would never run this cluster feature and would steer away StackWise as well unless I have extremely good justification for it.
Usually higher software complexity means lower MTBF and that is my experience running tens of 3750 stacks and hundreds of individual 3750 switches.
The newly introduced 3850 stack architecture seems much more appealing, as it's more closely designed to look like chassis based switch, you have two RPs and bunch of dumb linecards. But of course experience is thin on such a new solution.
As @Brett said, StackWise cables are required. Depending on what your goal is for the stack, you may be fine just creating an port-channel (Etherchannel) using up to 8x100Mb (800Mb) or 8x1Gb (8Gb) between 3750 switches. If you have certain 3750 models with 10/100Mb ports and 1000Mb uplinks, you could channelize up to 4 ports to get 4Gb.