Jack Powell was with the St. Louis Browns for ten seasons over two runs, and while he may have had a losing record (117-143), it was more of an indictment of the team he played for.
Playing at Third Base, Harlond Clift debuted in the Majors for the Browns in 1934, and he had a nice rookie year with 14 Home Runs and a .260 Batting Average. He did lead the American League in Strikeouts, however, but unlike many baseball players who have done so, he was able to reduce that part of his game, and would swat at flies less and draw free passes more.
George Stone finally found a home in the Majors at age 28, and with the St. Louis Browns, he would have a 187 Hit year (which led the American League) in 1905 as a rookie. Stone exploded in 1906, sweeping the Slash Line (.358/.417/.501) with 208 Hits. As the Browns did not receive that much attention then (and now in a historical context), Stone's accomplishments have not celebrated, but he remained a competent player until 1910.
Adam Jones was one of five players traded by the Seattle Mariners for Canadian Pitcher, Erik Bedard, in the Winter of 2008. Had it just been straight-up Bedard for Jones, the Mariners still would have lost the trade.