I saw him came.

No it is not correct. In fact, I am not exactly sure what you intend to say.

I saw that he came. Would imply that you noticed his attendance (at some event).

I saw him come. Would mean that you saw him arrive at some place.

I would prefer "I saw him arrive".

Thanks, maxdancona.

You have answered my questions.

I want to point out that the verb "to come" can be used in a sexual way to refer to the act of having an orgasm.

When I read your post... that was my first thought. We sometimes use "I think he came" ... to be a euphemism.

Where I live, "I come" means "I arrive" unless there is further context to suggest the sexual meaning.

Hi! Let me join in the conversation. Well, my mohter language isn't English, but I have always been being found some similar sentences in some textes, like "I saw him go," "I saw her depart," "I saw him do that," etc. And when I said some similar sentence to an English person, she protested against it, saying that "-ing" is needed, it can't be omitted. Is it possible that there are parts in the UK when omitting "-ing" in such cases is really unknown? And does it work only with the case of seeing someone and with personal pronoun? I mean if I can say: The people heard Peter shout.

What phrase would you use to refer to "reaching orgasm" if you were in polite company?

Such a matter is taboo. We do not let other people know about that. Only when a couple are engaged in the act do they talk about orgasm.