Pillows

Of course you can, & I do... I use an Eagle Creek size S compression bag (they last years, unlike Amazon products) to pack mine down small enough it doesn't take up much room. Why not experiment, see how small you can squish it? It's also inside a hypoallergenic pillow case cover. After forgetting my pillow in a domestic hotel & having them ship it back to me FEDEX, I switched to a bright blue pillow case, so it's quite noticeable.

Can I take a pillow on an international flight?

How big a pillow are you contemplating? and what cabin class?

Let's make sure we are all talking about the same thing.
Are you thinking you can take it as an extra item as well as the published allowance the airlines give? As in a carry on suitcase and personal item and ALSO a full size sleeping pillow?
Some of us condense the size and put it into one of our allowed bags and pull it out at our seat. Me, I stuff my winter coat into a pillow case and use that as a pillow on the plane.
Certainly smaller neck pillows are allowed. You've seen them, those donut shaped things velcroed to suitcase handles or around people's necks.