What do you have? Are you talking about The Old Republic? From the looks of things it will be like WoW. Not very high end graphics at all. A decent computer from the last 7 years with a mid level graphics card should run it just fine. You might not be able to crank up all the settings, but I am sure it will run in DX9 perfectly fine with rather old hardware.
MMO's are never made with high end stuff in mind. No need to go out and buy a new gaming computer.
Heck, even Mass Effect 3 won't be very graphics intensive since it's a console port. Battlefield 3 is an example of a game that will require some people to upgrade since it will be DX10 and DX11 only. That means only GPU's less than 5 years old can play it.
PC gaming is not like it used to be. Sure, there are some games like Metro 2033, Crysis, Shogun 2, etc. that are PC exclusive and very graphical intensive. Yet even then old computers can run them at lower resolutions.