Grew up in Texas with parents from Michigan, so I learned to have two favorite teams. Their top players from the 80's and early 90's remain some of my favorites:
Detroit:
Allan Trammel - face of the Tigers for ~15 years
Cecil Fielder - the year he came out of nowhere to hit 51 homers was magical to teenage me
Rob Deer - kind of tongue in cheek, but I had fun watching how low his average could go while still hitting 20+ homers
Texas:
Ruben Sierra - The best player on the team when I started following
Nolan Ryan - he was the MAN and about the only good thing the Rangers had going at the time
Julio Franco - just loved how he stuck around and played until he was older than dirt
Jeff Kunkel - One of the worst players to ever don a Rangers uniform, for some reason I always rooted for him and called him Uncle Kunkel.
Others:
Guys who played well for a long time with one team like Tony Gwynn, Cal Ripken, Jr., and Ozzie Smith
Orel Hershiser - his scoreless inning streak still amazes me; seems like a great stand-up guy
Joe Schlabotnik - gotta root for the underdog! http://peanuts.wikia.com/wiki/Joe_Shlabotnik