if i've got this correctly...
in the AL, we have Yankess (last WS win 2000, last played in WS 2003) in 1st vs. Tigers (last win 1984 and have not been in WS since) at wildcard.
Twins (1991, have not played in WS since) in 2nd place vs. A's (1989, last WS appearance 1990) in 3rd
in the NL, Mets (1986, thanks Bill Buckner, and last WS appearance in the 2000 subway series) in 1st vs. Dodgers (1988, have not appeared in WS since) at wildcard
Padres (never won the WS, last WS played 1998) in 2nd place vs. Cardinals (1982, last WS played 2004) in 3rd place.