They are both correct, grammatically speaking. However, they have slightly different meanings. I saw him crossing the road. ... suggests that you saw a male person in the middle of crossing the road (he was probably walking in the middle of the road toward one of the sides). But, you didn't necessarily see him get to the side of the road I saw him cross the road. ... suggests that you saw him do the entire action of starting on one side, walking across, and ending up on the other side.

they are the same.

Cross-ing may imply you see him do it while he's doing it. :) cross may imply he's already finished and on the other side, is still doing it, or, it can also mean you saw him across the street. I hope that helped.

I saw him cross the street is grammatically incorrect cross is a noun and not a active verb in this case , now you saw this person in action meaning you have to change the noun cross to a active verb which is crossing.