Minecraft will run on any system, but it depends on the stuff that you have on how many frames you will run minecraft at. Most likely you will be able to run it at atleast 20 frames per second
stnvegs is wrong, now more than ever not all computers have Open GL supported drivers especially on Win 8/8.1
As Ugion said I'd be concerned about Open GL support. You didn't specify the OS you have. The 9500 GT is 4 years old. If you have Windows 8 or 8.1 I'd be concerned whether or not there were proper drivers available for it.
CPU: Intel Pentium D
RAM: 2GB
GPU: NVIDIA GeForce 9600 GT
HDD: 200MB (Available) for Game Core Files
Java 6 Update 45
My Specs
CPU: Intel Core 2 Duo
RAM: 4GB
GPU: NVIDIA GeForce 9500 GT
HDD: 500GB
Java 7 Update 65
As you can see, my computer fits every minimum requirement other than the GPU. Can I still run Minecraft? Thanks.
As Ugion said I'd be concerned about Open GL support. You didn't specify the OS you have. The 9500 GT is 4 years old. If you have Windows 8 or 8.1 I'd be concerned whether or not there were proper drivers available for it.