Does it really matter? Easiest way, take a look at the sticker on your PSU, it will label each +12V output's max current separately.
This doesnt necessarily mean you have that many though, the majority of PSUs have a single 12 volt source and each rail is split off of this source with a current limit set for each branch, there are also ones that claim multiple rails but dont separate them at all and only claim multiple rails because thats what older spec wanted. Basically the number of rails you have is irrelevant, what counts is the total power available on them combined.
You can pull too much current from a rail, but if you have a single rail design then you dont have to worry about tripping individual rails, you do still have to worry about over drawing the PSU as a whole which can damage it. What PSU do you have and what are the other specs in your system?
You say you are looking to upgrade, what are you looking to upgrade to? General rules of thumb, a good 550W unit(~40A on +12V) will power any single GPU, a good 750W unit(~60A on +12V) will power a two GPU setup, these both leave additional power to spare to keep the PSU cool and efficient.
Wow, your current one definitely needs an upgrade. Most of your components run on the 12V rail, and your PSU only has 156W available to things running on the 12V rail.
I would suggest something more powerful than the 7600GS, maybe something like a 9600GT or a 4670 or a 5670, either of them would be significantly more powerful and wouldnt need a strong PSU. A good cheap one is the corsair 400CX, it will easily power a lower power card. http://www.newegg.com/Product/Product.aspx?Item=N82E168...
It may not seem all that cheap but realize that the super cheap PSUs have explosive tenancies and tend to take out other components when they go.
Thanks for the advice, looks like they have a 4670 that will work with my machine. Although they only list power supply requirements as 400watt min, doesn't say anything about the current needed. Thanks again.