Which registers are used for each data size in x86-64?

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Accepted Answer

Each general-purpose register has a name for every width: e.g. %rax (64), %eax (32), %ax (16), %al (8) — and the new registers use suffix letters: %r8, %r8d, %r8w, %r8b.
This is the naming system that lets one physical register be used at any of four widths. The original registers use distinct historical names, while the new R8–R15 registers use a regular suffix scheme that's much easier to remember.

Size
Original-8 example
New-register form

8-bit
%al, %bl, %sil, %dil
%r8b

16-bit
%ax, %bx, %si, %di
%r8w

32-bit
%eax, %ebx, %esi, %edi
%r8d

64-bit
%rax, %rbx, %rsi, %rdi
%r8

movb %al,  (%rdi)   # store 1 byte
movl %eax, (%rdi)   # store 4 bytes
movq %rax, (%rdi)   # store 8 bytes

Important reminder: writing the 32-bit form (%eax, %r8d) automatically zeros the upper 32 bits of the full register, while the 8- and 16-bit forms do not. This asymmetry is the single most common cause of "where did my upper bits go?" confusion.
Go deeper:

x86 (Wikipedia) — the per-width register naming, including the r8d/r8w/r8b scheme.

Size	Original-8 example	New-register form
8-bit	%al, %bl, %sil, %dil	%r8b
16-bit	%ax, %bx, %si, %di	%r8w
32-bit	%eax, %ebx, %esi, %edi	%r8d
64-bit	%rax, %rbx, %rsi, %rdi	%r8