Agreeing to free trade allows residents of those nations, those who pay the taxes and contribute every dollar necessary for the government to exist in the first place, to pay lower prices for goods due to increased foreign competition. Any policy which lowers the cost of living for a country's society is a good one, as it markedly improves their lives.
What has happened in the United States over the past several decades is the growth of the trade gap. We import many goods, but our exports have declined seriously. This has negative effects on the economy within the country. Manufacturing jobs, once a staple of middle class income, have largely been outsourced. When a country allows its citizens to import foreign goods but does not insist that its own goods be purchased, it creates an imbalance that lands squarely on the lower classes. This imbalance is, ultimately, not good for anyone.
No, countries should not being adopting trade agreements at all. In this day and age we have a global inter-connected economy that effects nearly everyone in the world. You would think with all this trade you would need more government headway to smooth over relations. It really just isn't the case. Companies have done a pretty good job of finding the markets they want to be in. Trade agreements hurt competition around the world, and make some countries strong at the expense of making other countries weak. Regulate companies within your own boarders, and let them do their own business abroad with neither help nor hinderence.