There were attempts at settlement made in the 1600's by Sweden. The Delaware River Valley, touching the states of Delaware, southeast Pennsylvania and southwest New Jersey, was home to Swedish settlers beginning in 1632. Their attempts at colonization were thwarted by the Dutch of New Amsterdam under Peter Stuyvesant in 1655. New Sweden was incorporated into New Amsterdam for a time.
Swedish settlements also existed on the Gold Coast and Ghana in West Africa. These possessions were held briefly however, as shortly after their founding in 1650, the Dutch and their Danish allies conquered their forts and thwarted the Swedish efforts at overseas expansion again in 1663.
These setbacks, and rivalries with neighboring states (The Thirty Years War, The Scanian War, The Great Northern War, The Second Northern War) left little in terms of resources or manpower for further overseas colonization. That's not to say the appetite for colonies was altogether absent. The Swedes were given St. Barts by the French and formed a West India Company in 1784. The island was later resold to France in 1878.