Quo Vadis (by I forget who)
And if you want to go way back, Aeneid by Virgil 
I forgot to mention that I read Silver Pigs by Lindsay Davis. And I’m actually re-reading Roman Blood now that I know who all the secondary characters are (I still haven’t read any other Gordianus book yet).
A good, but hard-to-find, book is also Barbara Hambly’s Search the Seven Hills.
I heartily join the chorus recommending Davis.
Pillar of Iron, by Taylor Caldwell
Two of Michael Curtis Ford’s historical fiction books are based in Ancient Rome. I haven’t read his latest, but his first was really good. My only problemwith his writing is that he always takes the loser’s point of view. For example, one of his books focuses on Mithridates’ struggle against Rome. And although he seems to get mediocre reviews, I really like what he writes.
Anyway, two of his four books that have Roman protagonists: Gods and Legions and The Sword of Attila. Like I said, I haven’t read Attila yet, but I liked Gods.
It’s more ancient Byzantium, but try H. N. Turtletaub’s historical novel Justinian.
I humbly recommend my own epic novel of ancient Rome, which is due to be published…well…some time after I finish it.
Of course that requires that I actually start writing it.
No fear, though, I have the whole thing set up in my head, and a decent library at home of books on Rome, Carthage, and the Second Punic War. Someday.
I’ve got a title, though, which is very reassuring.