Any benefits to running minecraft in a 64bit environment?
Solution 1:
Minecraft is written in Java, so it should "adapt" itself to both 32-bit and 64-bit systems (depending if you have a 32-bit or 64-bit Java runtime).
While Minecraft itself is not optimized for 64-bit, it will take advantage of JVM optimizations for 64-bit processors. Basically, this means more general-purpose registers available (16 in 64-bit against 8 in 32-bit, which means better machine code and less RAM access, improving performance) and larger addressable memory. On the other hand, since now pointers take up twice as much space, there is a little extra overhead for using 64-bit.
But you should also think about the operating system, as it will also take advantage of 64-bit improvements. If you have more than 2GB or 3GB of RAM, your operating system should be 64-bit, else it won't access all RAM (or will have a considerable overhead doing so). And if you have a 64-bit operating system, you should also go with a 64-bit Java Runtime for better performance (as other users already commented).
By the way, in my opinion, you should always go to 64-bit unless you have a very good reason to avoid it, like compatibility reasons (which is not this case).
Related question on StackOverflow: Does Java 64bit perform better than the 32bit version?
Wait a minute! I talked code written in Java, but how about native libraries? Like OpenGL support and OpenAL? They are available on both 32-bit and 64-bit versions, and the correct version will be loaded. And I can confirm that on my Linux 64-bit system, it loads the 64-bit version of those native Java libraries. (as an experiment, I've deleted the 32-bit versions and Minecraft still runs fine)
Solution 2:
Minecraft is not designed as a 64-bit application, and thus, while usable on a 64-bit OS, won't see any sorts of improvements from a technical standpoint.
However, if you also install the 64-bit java runtime environment, you may notice some slight performance optimization, but a 64-bit OS on its own will not have much of an effect.