I didn't search for long before finding this season: Rick Wilkins in 1993. A third-year catcher in '93, Wilkins had hit well enough after a promotion from the minors in '92 to win the job for '93. Even the most optimistic of Cubs fans couldn't have expected his season: .303/.376/.561, with 30 home runs in 446 at-bats. The next season, he hit .227 with seven homers; then he fell to .203 with seven homers and the Cubs shipped him out of town. Here's what's interesting: Even though Wilkins was hitting .191, the Cubs acquired Luis Gonzalez in that deal. The same Gonzalez who would eventually find his way to Arizona, where he would hit 57 home runs in 2001.
OK, back to Wilkins, Baseball-Reference WAR rates his '93 season as the best in Cubs history by a catcher. You know, a funny thing happened from 1992 to 1993. Yes, there were two expansion teams. But that alone doesn't explain the jump in offense: Run scoring went from 4.12 per game to 4.60, with the major league batting average increasing from .256 to .265 and the slugging percentage from .377 to .403. Lively ball? Everybody started using steroids at once? Wilkins was part of the offensive explosion.
There's Jack Armstrong, who started the All-Star Game in 1990 in his first full season in the majors but wasn't even in the Reds' playoff rotation by the end of the season, but I'm going with Pete Schourek. The Reds won the NL Central title in 1995 and Schourek was a big reason why, going 18-7 with a 3.22 ERA and finishing second in the Cy Young vote to a guy named Maddux. Two years earlier, Schourek had gone 5-12 with a 5.96 ERA for the Mets. Schourek's season wasn't a complete fluke, as he had a 160/45 strikeout/walk ratio and a .271 average on balls in play that, while low, wasn't ridiculous or anything. He was a good pitcher, at least for that one season. He was never really completely healthy after that (three elbow surgeries) and pitched through 2001, but usually ineffectively.
Bill Hall is still floating around the majors (barely), essentially because he had a great season back in 2006. As Milwaukee's shortstop that year he hit .270 with 35 home runs -- the only shortstops in the past 50 years to hit more home runs in a season are Alex Rodriguez, Rico Petrocelli and Rich Aurilia. It proved to be a fluke season as Hall combined for 29 home runs the next two seasons and drifted into journeyman status, going from Milwaukee to Seattle to Boston to Houston to San Francisco and to Baltimore in 2012 (for seven games).
Here are Oliver Perez's ERAs from 2002 through 2010: 3.50, 5.47, 2.98, 5.85, 6.55, 3.56, 4.22, 6.82, 6.82. One of those is most unlike the others. While Perez had a couple decent seasons with the Mets, his 2004 season with the Pirates stands out like that patch of white on Rasheed Wallace's hair. He went 12-10 with that 2.98 ERA, striking out 239 batters in 196 innings. It was his age-22 season, and the Pirates believed they had a staff ace in the making. Instead, Perez was never able to harness his control in Pittsburgh. He re-emerged in the Mariners' bullpen last year, and since he's still just 31 might have a long career as a lefty reliever.
How about Fernando Tatis? In 1999, Tatis hit .298 with 34 home runs, 107 RBIs, 104 runs, and .404 OBP. Not a bad season for a 24-year-old third baseman. That April, he accomplished one of the most amazing feats in major league history, hitting two grand slams in one inning (both off Chan Ho Park). He battled various ailments, spent 2004 and 2005 out of the majors, and while he returned for a couple decent seasons as a utility guy with the Mets in 2009 and 2010, that 1999 season remains his big shining moment.