He has been the most mis-cast actor I've ever seen.
He has literally -ruined- several otherwise great movies (Dracula, Much Ado About Nothing, etc.) But that's more the fault of producers who wanted to cash in on his star-power.
That said, he was perfect for The Matrix and he was good in this.
In short: Like many He is a one-dimensional actor. And he's fine for the movies he's fine for.

This movie is set in a dark period in Constantine's life. Midnite even said "You
were
John Constantine", implying that he's not the man he used to be. In my head, pre-cancer Keanu Constantine is basically an American version of the character from the comics. A couple of things that bugged me about the movie is that a) Constantine is more of an exorcist that a mage. I don't even think that "magic" was even mentioned or alluded to in this movie. B) He wasn't in his recognisable coat. I don't care if his hair isn't blond, or that the accent isn't right, but the coat is part of his uniform.

Apart from flat and unemotional, he's totally not the character of Constantine. John Constantine is a british careless rebelious character. Reeves is not even far from it.

I am a big fan of Keanu and outside of Bill and Ted I would recommend for his acting alone
Rivers Edge
Permanent Record
The Night Before
Brotherhood of Justice
And just because he is awesome in
Speed
Point Break
Parenthood
I Love You To Death

Yeah I don't get the hate either. Keanu is just COOL and acts a lot through his voice. People say he can't act, but he can play certain "badass cool" roles very very good, that are often played really bad by other actors. He doesn't have a lot of range, but he plays some characters really well.
He is a bit like the "mysterious women" a stereotype for a seductive female that doesn't give anything away about here, so that others will imagine their own fantasies on her about what they wish.