This is something I've been wondering. I could see it being Superman or Dick Grayson. I'm partial to Grayson myself but I can see why him and Clark would be tighter. Of course, if you consider stories where Bruce ends up becoming a major jackass (Batman Beyond, TDKR), then no one would be the answer but in general, it would have to be between these two.
Clark- Partner in the Justice League, do a lot of team ups, high level of trust between each other
Dick- Former sidekick turned partner, practically brothers when Nightwing grows up (w/ the exception of Beyond which was just nasty)