How do arithmetic instructions affect the flags register?

Question

Accepted Answer

Most arithmetic and logical instructions set the condition flags as a side effect — but lea and mov set nothing, and inc/dec notably leave the carry flag alone.
Knowing which instructions touch flags is essential when reading code, because a conditional jump depends on whatever last set them.

Instruction
Flags modified

add, sub, cmp
ZF, SF, CF, OF

and, or, xor, test
ZF, SF (CF and OF cleared to 0)

inc, dec
ZF, SF, OF (CF unchanged!)

lea, mov
none

After cmp a, b (which computes b − a):

Condition
Unsigned test
Signed test

b == a
ZF=1
ZF=1

b < a
CF=1
SF≠OF

b > a
CF=0 and ZF=0
SF=OF and ZF=0

add %rbx, %rax   # sets all four flags
jo overflow      # OF=1 → signed overflow
jc carry         # CF=1 → unsigned overflow
jz zero          # ZF=1 → result was zero

Gotcha: because inc/dec don't touch CF, multi-word ("bignum") arithmetic that relies on carry must use add $1 / sub $1 instead.
Go deeper:

FLAGS register (Wikipedia) — the ZF/SF/CF/OF condition flags set by arithmetic.
 Felix Cloutier — ADD — concrete per-instruction flag effects for ADD.

Instruction	Flags modified
add, sub, cmp	ZF, SF, CF, OF
and, or, xor, test	ZF, SF (CF and OF cleared to 0)
inc, dec	ZF, SF, OF (CF unchanged!)
lea, mov	none

Condition	Unsigned test	Signed test
b == a	ZF=1	ZF=1
b < a	CF=1	SF≠OF
b > a	CF=0 and ZF=0	SF=OF and ZF=0