I do, usually.
It depends what I'm going to do withthem. If they're going to be cubed and cooked gently for a sauce then I'll always salt them.
If I'm going to fry them and I have time, I'll salt them because it decreases the amount of splatter!
On the other hand, if I'm going to roast the crap out of them I don't always bother.
I think it makes a difference, but maybe I'm just very impressionable
ETA: the point is to leech out some of the slightly bitter juice- I definitely makes a difference for slightly past their best aubergines, but for fresh beauties I'm not so sure.
And it does seem to firm up the flesh a bit, but I've never bothered to halve an aubergine and make the same recipe with salted and unsalted versions...