1900s - 1970s: 1976 MSA Isalys Jerry Morales I'v got an entire post about this set here. Morales was at his career peak in 1976. He hit a career high 16 HRs in 1976 and his average was in the mid .270s.
1980s: 1989 Fleer Glossy #631 Rafael Palmeiro All Star Palmeiro has two cards in the 1989 Fleer set, this All Star card and his base card. He also has a card in the traded set because he didn't spend the 1989 season with the Cubs. He was traded to the Rangers before the season in a deal that brought Mitch Williams to the Cubs.
1990s: 1994 Stadium Club #355 Dan Plesac The lefty from NW Indiana pitched in 54 games for the 1994 Cubs, all out of the bullpen. He was 2-3 with an ERA of 4.61. The team brass was so impressed by this that when he became a free agent after the season, they didn't bother to offer him a contract.
2000s: 2008 Factory Team Set #CHC6 Carlos Marmol This is one of three different cards of Marmol from Topps in 2008. He didn't make the base set, but had a card in Update. He was also included in the special Cubs version of the Factory Complete set that included 5 bonus cards, of which Marmol was one.
2010s: 2014 Donruss #81 Travis Wood Here is Travis Wood in all of his logoless glory on Donruss 2014. I don't think it has happened very often that the RNG has picked a card from the current year. Wood is off to remarkably unremarkable start to the 2014 season. He is 4-4 with an ERA of 4.61. He was the Cubs' lone All Star last year. I don't think that he will be on the team this year.