Although the actually specifications for the game have not been announced. Here is a list of suspected specifications based on specification for other MMORPGs such as DAoC [Dark Age of Camelot] or Everquest who is made by the same people that are working on SWG.

Minimum Specifications
Operating System - Windows 98/ME/2000/XP
Processor - Pentium III 500 MHz [Or equivalent processor like AMD Athlon]
RAM - 128 MB RAM
Graphics Card - Direct3D compliant graphics card with 16 MB RAM and hardware T&L (such as GeForce 2 etc)
Sound Card - DirectX 8.0 compatible sound card
Modem - 56k + Internet Connection
CD-ROM - 4x Speed CD-ROM
Hard Drive Space - Around abut 600MB

The most likely details on this list that are likely to change are the HD Space, as it is rumored that SWG will use a more efficient method of storing data

Recommended Specifications
Operating System - Windows 98/ME/2000/XP
Processor - Athlon XP 1200+ [Or equivalent processor like Intel Pentium 4]
RAM - 512 MB RAM
Graphics Card - Direct3D compliant graphics card with 64 MB RAM and hardware T&L (such as GeForce 2 etc)
Sound Card - DirectX 8.0 compatible sound card
Modem - 56k + Internet Connection
CD-ROM - 16x Speed CD-ROM
Hard Drive Space - Around abut 1.5 GB +

Again this is just and educated guess, and specifications should be announced nearer release, maybe being announced at beta. The next two specifications are not as important but if you are running these then sit back relax, as SWG will be looking good on your computer.

E3 Specifications
Operating System - Windows 98/ME/2000/XP
Processor - 1.7 GHz [Not known what brand it was, most likely Pentium IV]
RAM - 512 MB RAM
Graphics Card - GeForce 3 [most likely the Ti series]

Not much was known about the PC's running the game, but it did look good. And had quite a lot of detail in it.

'Ultimate' Specification
Operating System - Windows 98/ME/2000/XP
Processor - Athlon XP 2000+ [Or equivalent processor like Intel Pentium 4]
RAM - 1024 MB RAM
Graphics Card - Direct3D compliant graphics card with 128 MB RAM and hardware T&L (such as GeForce 4 etc)
Sound Card - DirectX 8.0 compatible sound card
Modem - ADSL [or similar speed] connection
CD-ROM - 52x Speed CD-ROM

If you are running something similar to this then SWG will be flying on your PC. An important note to make about all of these specifications, at E3 it was said that all of the graphics are scalable. You can turn everything on and off, make it more detailed etc. They also said that they can turn up the options so high that no computer known to man could run it. They have done this for 2 reasons
1] So that they can get a good period out of the game
2] So that low end spec users can turn alot of the features off and play at a good speed.