MapXtreme 2008 is finally supported on 64-bit Windows x64, which is important for many of the reasons outlined in the Benefits of Windows x64 Editions, but most significantly because it gives you a much larger Virtual Address Space. MapXtreme ASP.NET web applications can typically run into the 800MB to 1200MB process memory limit on 32-bit Windows described here, and larger Virtual Address Space will alleviate this by allowing up to 2800MB.
MapXtreme 2008 doesn't get to take full advantage of the Virtual Address Space available in 64-bit Windows, however, as it is still 32-bit code and so needs to run in Windows-on-Windows, WoW64, emulation mode. If it was 64-bit code, the process memory limit would be around 70% of RAM + Pagefile. As mentioned in this article though, if a .NET process is multiple GB in size, "it can become very difficult for the Garage Collector to keep up with the memory as Generation 2 will become very large", so it is probably best not to let it get that big! Besides, MapXtreme will probably not have a 64-bit codebase until after the end of the 2009 calendar year, so you needn't worry about that for a while.
One last thing, if you are compiling a MapXtreme Desktop application, and you want to have all 2800MB meomory available to your application, then you will need to check that the IMAGE_FILE_LARGE_ADDRESS_AWARE flag has been set on your executable. This flag can be set programmatically, or by the compiler, or you can alter the File Header after compilation using a PE editor such as CFF Explorer. As you can see below, the w3wp.exe process that runs your ASP.NET applications already has this bit set, so there is nothing to do for your ASP.NET web applications.