At the moment, the answer is a resounding "it depends". Specifically, it depends on the OS and which version of D.
DMD, or the Digital Mars D compiler, is the reference implementation and offers absolutely no 64-bit support. Walter Bright, the language creator, has indicated that this is a high priority and he has every intention of adding support for this after D2 is finished. (D2 will be finished relatively soon, since Andrei Alexandrescu's book "The D Programming Language" is slated to be released soon.) However, he has indicated that due to linker issues, the first few versions will not support 64-bit on Windows.
For D1, 64-bit support is great on Linux and Mac if you use LDC, which is a D compiler targetting LLVM. For Windows, the GDC compiler, which targets the GCC back end, has been resurrected but is several versions behind the curve. On D1 this isn't terribly important since the language spec is fairly stable.
For D2, 64-bit support is currently basically non-existent. The aforementioned GDC does support it, but D2 has been evolving rapidly and GDC is too out of date to be useful here. Most non-trivial code written for version 2.015 (the latest GDC supports) probably won't even compile on version 2.040 (the latest version of DMD) and vice-versa.
Edit: As of today, June 21, 2010, there are some commits in SVN towards 64-bit support for DMD. These are far from a working compiler, but the point is that it's underway.