In single player my games tend to turn into turtles. I first scout and identify the 'turtle point' at the map at which there is no passage from one side or the other except through it or through the pirates, rush aggressively to acquire it, typically fight it out with the AI to acquire it, starbase it and completely fortify it, backfill the other colonies, and then develop my economy until it dwarfs the AI's. Once I've attained a massive economic advantage I build up my fleet and then finish the game in a very predictable manner:
First, I wait until the pirate bid comes up and win it. I use scouts to identify which planet they go after as soon as it's determinable.
Second, I pay the pirates 40,000 credits to launch a 1000 supply raid on a different planet than the first.
Third, once I see the massive pirate raid in transit I launch my entire fleet (usually over 1300 supply by this point) on a third planet.
The overwhelming force typically spreads the AI's forces far too thin and takes out three of his border planets. So far no AI has recovered.
I wish the random map generator would generate more maps without turtle points. It'd probably make me a better player to have to win without turtling like this, it's just so effective, at least against hard or lower -- haven't tried my hand at unfair yet. I understand the higher difficulty levels get massive hardcoded economic advantages, though... so perhaps it'll stop being such a good strategy when I move up there. Although, sometimes the turtle point is in a massively disadvantageous position for you and you have to play aggressive or lose because the AI gets 2/3rds of the map. And that's fun and hard to deal with.
Also, having recently upgraded from vanilla to diplomacy I have to say kudos to the devs for upgrading the AI. I was curbstomping the vanilla hard, but the diplomacy hard is making me sweat at spots.