SATA III?

It would be a hardware upgrade to get the full speed, but it is backwards compatible, so you can plug a 6Gb sata drive into an older port, and it will run fine at the lower speed.

But are the actual Motherboards compatible with the SATA III technology, or I would have to buy a new one?

you'll need a new motherboard that has the SATA III controller chip, whenever that gets released. but really im not sure hard drives are even at the edge of SATA II speeds so i dont know how much of a difference it makes.

SATA II nor III does not exist. That naming has been abandoned by SATA-IO long ago. Calling it SATA II or III can just mean SATA.
The correct way when speaking about SATA rev. 3.0 is "SATA 6Gb/s" (note the small case 'b' which indicates bit and not byte).

Anyone who tells you SATA II or III is speaking bollocks.

As all above posters have said, SATA 6Gb/s requires a new SATA controller, either as integrated into chipset/southbrige of motherboard or as expansion card.

Are current SSD drives pushing current SATA data rates? Should I wait on SATA 6Gb mobos to be out before I build my next system if I plan on using SSDs?

There are already SSDs made with PCI-e interface for 2GB/s+ full duplex bandwidth, actual speeds 1GB/s+. But these are expensive enterprise class products, not available for mortals like you and i. But this kind of technology could be commonplace and would be logical for the system disk. See here for an example:

http://en.expreview.com/2009/06/06/super-talent-shows-o...

But chipsets with 6Gbps SATA and also USB3 (10 times faster than USB2; 4,8Gbps) are coming with the next generation AMD 800-series chipset, and nVidia/Intel will likely follow. Another feature is Powered eSATA, removing the need for seperate power plug for eSATA devices. One cable supplies both data and power.