Considering how long you've been waiting for the StarCraft II beta, it would be a shame if your computer ended up being unable to run it. Today Blizzard released the recommended and minimum requirements.

Minimum

• Operating System: Windows XP / XP64 (Service Pack 3), Windows Vista / Vista64 (service Pack 1), Windows 7 Home Premium
• Processor: Intel Pentium IV 1.3GHz, AMD XP 1500+
• Memory: (Windows XP) 512mb, (Windows Vista) 1024mb, (Windows 7) 1024mb
• Graphics: 3D graphics processor with Hardware Transform and Lighting with 32 MB VRAM, such as an ATI Radeon 7200 or NVIDIA GeForce 2 class card or better
• Hard Drive: 15Gb (of free space)
• DirectX: DirectX9.0c

Recommended

• Processor: Intel Pentium D, AMD 64 X2
• Memory: (Windows XP) 1024mb, (Windows Vista) 2048mb, (Windows 7) 2048mb
• Graphics: 3D graphics processor with Vertex and Pixel Shader capability with 128 MB VRAM, such as an ATI Radeon X1600 or NVIDIA GeForce 7600 GT class card or better

"The final requirements for StarCraft II have not yet been determined; due to ongoing development the minimum requirements listed above are subject to change at any time," states Blizzard. Still, this gives you a pretty good idea of what you'll need for the retail version.