It may be a shorter list of those that aren't.  Certainly most countries are involved in some protectionism and subsidies to some industry or another.  The entire defense industry is one massive form of subsidy.  Agriculture is largely subsidised in developed nations and in many developing nations.  Individual industries or companies can enjoy subsidy by way of targeted tax breaks, or outright cash incentives.

Back to the original question: Do we gain more by sending jobs to other countries where the labour is cheaper?  

Its a very interesting question that often polarises people along ideological lines.  From a pure economics point of view protectionism is bad, and letting cheap labour take the jobs is better for the wider economy as a whole as prices are kept down while profits kept up.  win all round.  But from a social-economic point of view, where peoples livelihoods are considered of course its not so black and white with winners and losers.  

The idealist would hold that people can skill up and take better, less manual jobs, and we have more leisure time.  The realist will note that leisure time costs money (what can you do for free these days? not alot), there aren't enough "better" service/office jobs to go round, some people dont have the skills and if we are honest aren't going to no matter how good you try to educate (face it people have different abilities and aptitudes).  So some people will be left behind.  Protectionism is ultimately an attempt to redress this imbalance, but its is contrary to all society really wants (all the benefits of free trade), so it gets hidden from view with politicians, and most economist, pretending it isn't going on.