Not really. You'd only see a boost in speed moving a 240GB Sandforce-based drive or anything from an Indilinx Everest 2-based 128GB drive on SATA 6Gb/s. For most other drives, 3Gb/s SATA speeds are perfectly fine.
SATA 2 SSD usually max out at about 250MB/s. Still very fast and good access speeds.
Normal mechanical hard disk's usually give about 150MB/s but with much slower access speeds.
If your motherboard does not support SATA 3 get an PCiex4 add on card.
SATA 3 is generally also backwards compatible with SATA 2 meaning your SATA 3 SSD will run on SATA 2 but just not at it's full potential.
The only thing that you'll lose out on when you run a SATA III drive on a SATA II port is when you do sequential read/write operations. I can't verify this, but I'm pretty sure you can still reach the max I/O per second on a SATA II port.
I'd suggest that you go for a SATA III SSD, even if you have only SATA II ports on your motherboard.