I wouldn't say I have a favourite game in the series as such, but I love the different ideas and concepts that each entry brought to the table.
You can't go wrong with the classic stealth approach of the original, Pandora Tomorrow and Chaos Theory.
I haven't played Double Agent, so I can't comment on that.
I loved the style and presentation of Conviction, very satisfying and fast paced panther-like gameplay, and one of the few games I've played in which you can feel just how legitimately terrified the enemies are of you. Special shoutout to those brutal interrogation scenes.
I know Blacklist wasn't well received, but I thought that the level design and progression was overall superb in the sense that the Ghost, Panther and Assault playstyles were all viable - an approach which carried over to Watch Dogs 2 which quite frankly didn't get enough credit for. That said, the game was a bit too easy, and the co-op missions were a bit iffy and lacklustre compared to Conviction's.