I dont know all of their nominees but the ones I do know are...

Singles
2001: It's My Life: Best Rock Performance by a Duo or Group
2003: Everyday: Best Pop Performance by a Duo or Group with Vocal.
2004: Misunderstood: Best Pop Vocal Performance by a Duo or Group
2007: Who Says You Can't Go Home: Best Country Collaboration with Vocals
2008: (You Wanna) Make a Memory: Best Pop Performance by a Duo or Group with Vocal
2010: We Weren't Born to Follow: Best Pop Performance by a Duo or Group with Vocal

Albums
1991: Blaze of Glory: Best Song Written Specifically for a Motion Picture or for Television
2001: Crush: Best Rock Album
2008: Lost Highway: Best Pop Vocal Album

Video
1997: Live from London: Best Music Video, Long Form

The only win i am aware of is WSYCGH.