Minimum Requirements:
CPU: 1.5+ GHz multi-core processor, 2.0+ GHz single-core processor
RAM/Memory: 1.0+ GB for Xp, 1.5+ GB for Windows 7-32 bit, 2.0+ GB for Vista/Mac OS, 3.0+ GB for Windows 7-64 bit
Graphic card: Must support OpenGL 1.4 or better (if the computer is a laptop and uses an Intel Graphic Processor, check here, otherwise if it is from Nvidia/Ati, you should be fine)there is another variable in this that affects gameplay so no additional info until then
Hard Drive Space: 80+ MB of free space (might need more as Notch might add more stuff later on)
Recommended Requirements: (game should be running at least 60 fps, or 30 fps when it is loading chunks)
CPU: 2.0+ GHz multi-core processor, 2.5+ GHz single-core processor
RAM/Memory: 2.0+ GB for Xp, 3.0+ GB for Vista/Win 7/Mac OS, 4.0+ GB for all 64-bit Operating Systems
Graphic Card: ATI/Nvidia independent card that support OpenGL 2.0 with 128+ MB of dedicated G-RAM
Hard Drive Space: 256+ MB of free space
A relatively decent desktop you can get for about $500 USD should have all these requirements met
Certain Notes and Calculations:
RAM/Memory: run your computer on Safe-mode (Windows only) and see how much resources it needs. Add about 750 MB on that and around to nearest 0.5 GB and that should be roughly what you need (with some overhead room for some people)
Graphic Card: there is still a lot of unconfirmed information that needs to be sorted and analyzed, so it's more of a guideline than a requirement
Hard Drive Space: 30 MB is for the resources and etc that allows Alpha to run, 50 MB per world you will generate (50 MB is quite a lot of area for you to work on)
if you have a computer that can run minecraft and is worst than the setup i posted above, post it and i will see if it is doable
if you have certain components that you have no idea what it is or anything specific, try using CPUZ