1950s / 1960s: 1956 Topps #179 Harry Chiti Weird--I just showed this card yesterday, and the RNG picks it today. It's Chitipalooza! He was a part-time catcher for the Cubs in 1956, getting into 72 games. His average was kinda chiti--only .212.
1970s: 1979 Fritsch One Year Wonders #54 Don Eaddy The card is from 1979, but the player is from 1959. The card comes from one of three sets of One Year Wonders put out by card dealer Larry Fritsch. The sets feature a bunch on guys from the '50s and '60s that have a very brief career. Eaddy was a player in the Cubs' chain from 1955-1964, though the '57 and '58 seasons were lost due to military service. He played briefly with the Cubs in 1959, going 0-1, though he did play in 15 games. Most of his appearances were as a pinch runner, and he did score a run in one game.
1980s: 1989 Classic Blue #216 Andre Dawson This card has a nice shot of the Hawk leaning over the plate, waiting for the pitch. He has a stance that I could probably recognize even if his face was hidden.
1990s: 1993 Donruss #400 Frank Castillo. Castillo spent most of the 1993 season in the Cubs starting rotation, getting the ball in 25 games. The results were unspectacular: a record of 5-8 and an ERA of 4.84.
2000s: 2010 Bowman #129 Derrek Lee I miss good 'ol D-Lee. By the time this card came out in 2010, Lee's career with the Cubs was just about finished. The traded him to the Braves on August 18.