1) Dragonforce: Herman Li cites Sambora's solos as the first he would hear every now and then as a child, which inspired him initially. Sam Totman said something to the effect of "We just play Bon Jovi solos, just at a faster tempo"
2) Nickelback: Ouch! But seriously, their first 3 records are top notch pop rock. Chad Kroeger loves him some BJ.
3) 3 Doors Down/Aaron Lewis of Staind/Brent Smith of Shinedown/Corey Taylor of Slipknot/Daughtry/Alexi Laiho of CoB have all covered Wanted Dead or Alive, which is perhaps the most respected song in the Jovi catalog.