How does the IA-32 (32-bit) calling convention differ from x86-64?

Question

Accepted Answer

IA-32 passes all arguments on the stack rather than in registers — which is the main reason x86-64 calls are faster.
The two conventions differ most in where arguments live, and that difference drove a real performance gain when 64-bit arrived.

Aspect
IA-32
x86-64

First 6 args
stack
registers

Args 7+
stack
stack

Return value
%eax
%rax

Callee-saved
%ebx, %esi, %edi
%rbx, %rbp, %r12–%r15

Caller-saved
%eax, %ecx, %edx
many

Frame pointer
usually %ebp
optional

In IA-32 you constantly see arguments fetched relative to %ebp after the standard push %ebp; mov %esp,%ebp prologue:
movl 8(%ebp), %eax    # 1st argument
movl 12(%ebp), %edx   # 2nd argument
movl 16(%ebp), %ecx   # 3rd argument

Why x86-64 is faster: memory is much slower than registers, so passing the first six arguments in registers — and having twice as many registers to work with — significantly speeds up function calls. (Recognizing stack-relative N(%ebp) argument access is also a quick way to tell you're looking at 32-bit code.)
Go deeper:

x86 calling conventions (Wikipedia) — contrasts stack-based IA-32 with register-based x86-64.

Aspect	IA-32	x86-64
First 6 args	stack	registers
Args 7+	stack	stack
Return value	%eax	%rax
Callee-saved	%ebx, %esi, %edi	%rbx, %rbp, %r12–%r15
Caller-saved	%eax, %ecx, %edx	many
Frame pointer	usually %ebp	optional