I have been running Anim8or on Win 7 with no problems whatsoever, on both 32-bit (at work) and 64-bit (at home). Windows 7 has a couple of tools that allow it to run older software. To start with, right-clicking on the Anim8or icon allows access to a compatibility wizard that, in most cases, is able to resolve any issues that might occur. I did have to do this for Anim8or on both versions of W7 but it takes about a minute and has worked perfectly. At work I needed to run old versions of Corel graphics suite and the wizard could not resolve compatibility issues, I resolved this by running an XP virtual machine (all free downloads from Microsoft) with no further compatibility issues at all. The virtual machine runs as a window within W7 and will run anything that runs on XP. Not all systems are capable of running VM's, you shouldn't need it to run Anim8or but it is worth making sure your new machine is able to before buying.
davdud101: That system should be making mincemeat of Anim8or... the processors will hardly be working during modelling, rigging etc. Bear in mind however, Anim8or's renderers will be slow on any system as they do not support multi-threading. Rendering in Anim8or will have one of your 4 processors about 50% utilised at the most, the other processors will be twiddling their thumbs. Unfortunately there's not a lot you can do about this, it's just the way the renderers work.