Ace Combat 5.
I love the Ace Combat games, I love them so much, in fact, that there is an Ace Combat 2 Phoenix tatooed on my right bicep.
I love 5 so much, because it was the first one of the games that really dived into the idea of having a parallel/alternate Earth setting, and introduced more sci-fi and character-based elements.
Admittedly the story is a little choppy and unintentionally humourous, with some of the angsting by the characters, but I will take that story any day over the generic 'Oh Noes, Teh RUSSIANS ARE INVADING!' of modern shooters and sims.
It reminds me of an anime - which is meant as a compliment - and I'd say that it's one of the strongest entries of the series, followed by it's prequel/sequel (it was released after, but is a prequel story-line wise) Ace Combat 0.
Both have the largest amount and variety of missions, spread over the largest part of the game world. They have the best music (IMO), and the widest selection of aircraft.
The way the story plays out with your character at the focus of things, the rise and fall of events and how 'you' end up at the pivot of things is something I love, and what makes them great games for me - despite the fact they're both PS2 games.