This depends on your needs. MySQL is deployed in a variety of environments, ranging from Celeron shared-host machines with a single HD and 512Mb of RAM to multi-processor 64 bit systems with RAID 10 and over 16Gb of RAM. The actual system you deploy on will depend on your needs and budget.
If you want minimum specs, look to provide MySQL with around 100Mb of RAM. MySQL is not particularly processor-intensive, so any recent processor should do. Hard-drive space will depend on the size of your data.