I understand that it is annoying that, through no fault of your own, your cars get grassy and you have to clean them but I think it might be a bit strange to ask your neighbour to wipe them down. The best solution would be to put up a tarpaulin to protect your cars.
Why stop there? I was going to recommend giving him a new, aptly earned nick name of “no knees neighbor ned.”
Put up some kind of short wall to protect your cars. He’ll figure it out or he won’t, either way, your cars will be fine.
Were it me, said short wall would be attractive to the eye on my side, and hideous on his! 
my WAG? your neighbor knows exactly what he is doing, he knows how to switch it up so the grass stays within his own yard, so ask him nicely to stop. Or on lawn mowing day go outside and hang by the cars, get the garden hose ready to rinse off the cars as he passes, let him feel the spray.
This is definitely worth mentioning if you bring it up with them. Makes it seem like a more pressing concern when it’s about the potential for damage.
It’s bad advice to ascribe intent when you really have no idea. When I was a teenager my mom made me do all the mowing, and I would never have thought to pay attention to where the grass was flying. Mowing is fairly dirty, hard, hot work. And most people just want to get it over with as fast as possible.
Honestly it’s not a big deal, I would think the grass would blow off when you start driving. But if it bugs you, put up a wall or a tarp.
I don’t understand most of these answers. Why wouldn’t one speak to one’s neighbor in a case like this?
There is an easy solution - turn the mower the other way. Why not request that?
It’s likely that your neighbor doesn’t realize that he’s doing it. He’ll probably apologize and run the mower the other way. Problem solved. If he’s an ass, then you can consider doing stuff like putting up a screen. Why start with the more expensive and difficult solution?
There’s a lot of passive aggressive arsehole solutions here.
Just have a friendly word - ask him to either run the mower the other way, or offer to move the cars …
no big deal needs to be made of it
…and preclude the rare-but-not-impossible mower-throwing-a-chunk-o-something-that-dents-the-car liabilities and arguments.
–G!
I’m looking over…
…–Kevin Gershon
… 
… [also on Dr. Demento’s 25th Anniversary Collection]
It’s slightly less passive-aggressive than other suggestions; one hopes the neighbor will instead modify their own mowing behavior when asked (somewhat) nicely.