I was one of those weird users who used the 64-bit version of Windows XP, with what I'm pretty sure was an Athlon 64 X2, both the first 64-bit chip and first dual-core one that I had.
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The only issues I came across were artificial blocks. Some programs would check the OS version and give an error just because. Even the MSN Messenger (also by Microsoft) refused to install by default; I had to patch the msi somehow to install it anyway. And then it ran without issues, once installed.