I also have a new computer with Windows 7 64-bit.
a Dell T7500, 12 GB Ram, 6-core, Intel Xeon X5650, 2.67 GHz with an nVidia Quadro graphics card.
AutoCAD 2012, 64-bit is installed. I have had a few crashes, that I attribute to the Drawing Tab utility. But what I find odd is that there are some commands that this "Fast" machine takes a long time to process. Inserting a block from a Tool Palette takes several seconds, where before it was almost instantaneous. The other one was I had a 3D solid that I had imported from Solidworks and I ran the Flatshot command on it and it took literally 30 minutes to finish it. In AutoCAD 2012, 32-bit on WinXP Pro it would take 10-15 minutes, but half the time I couldn't continue working very long otherwise the computer would crash, but with Win7 it doesn't crash, it just takes a long time.