For both leagues, there are various awards:
Gold Glove
Silver Slugger
Rookie of the Year
Manager of the Year
Cy Young
MVP
I think these are pretty much the only awards most of us care about. I'll list my candidates later but would appreciate some input from the baseball fans who are still lurking around.
NL GG: C - Molina, 1B - Freeman, 2B - Barney (the streak and he's made 74 more outs than Phillips in just 5 more innings - most in the NL), 3B - Headley, SS - Reyes, OF - McCutchen, Bourn, Victorino
AL GG: C - Avilla (would like to give it Suzuki, but he's barely played half the season), 1B - Teixeira (AGon's until he was traded to the NL), 2B - Cano, 3B - Moustakas, SS - Hardy, OF - A Jones, A Jackson, Brantley (Span close behind).
NL SS: C - Posey, 1B - Goldschmidt, 2B - Hill, 3B - Wright (though ARam and Headley can catch him), SS - Desmond, OF - McCutchen, Braun, Holliday,
AL SS: C - Mauer (with Pierzynski close behind), 1B - Fielder (Pujols gaining), 2B - Cano, 3B - Cabrera, SS - Jeter/Andrus (tied right now IMO), OF - Trout, Hamilton, Willingham, DH - Encarnacion (Butler close behind).
NL RoY: Frazier
AL RoY: Trout
NL MoY: Bochy or Hurdle (if the Pirates get into the playoffs, it's Hurdle all the way)
AL MoY: Showalter or Melvin (whoever gets to the playoffs. edge to Showalter if both get there)
NL CY: Dickey (Cueto very close behind)
AL CY: Price (honorable mention to Felix - who comes short in wins due to being on a terrible team)
NL MVP: McCutchen (Posey a close 2nd right now, honorable mention to Braun)
AL MVP: Cabrera (Trout a very close 2nd, honorable mention to Hamilton)