In this paper, we study conditions guaranteeing that a product of ideals defines a Golod ring. We show that for a
3
3
-dimensional regular local ring (or
3
3
-variable polynomial ring)
(
R
,
m
)
(R, \mathfrak {m})
, the ideal
I
m
I \mathfrak {m}
always defines a Golod ring for any proper ideal
I
⊂
R
I \subset R
. We also show that non-Golod products of ideals are ubiquitous; more precisely, we prove that for any proper ideal with grade
⩾
4
\geqslant 4
, there exists an ideal
J
⊆
I
J \subseteq I
such that
I
J
IJ
is not Golod. We conclude by showing that if
I
I
is any proper ideal in a
3
3
-dimensional regular local ring and
a
⊆
I
\mathfrak {a} \subseteq I
a complete intersection, then
a
I
\mathfrak {a} I
is Golod.