Dragon IS a memory pig. I've cited minimum specs on the Wiki page and can honestly say it's not worth using if the machine doesn't meet the minimums.
Dragon Minimum PC Specs
My own machine is: a QuadCore 2.4 GHz with 4.0 GB RAM, under Windows 7 Ultimate.
It's older, and I'll be getting a new one in July of this year (hopefully watercooled because I multi-task like a demon and have yet to find a system that can keep up with me).
I hope that helps.