Annex Them!
Pros:
If you know an event is coming that allows you to make their provinces your national provinces, then this would eventually allow you to use those provinces to the fullest: no manpower or IC penalties.
You can direct the building of stuff in their provinces ie an airport (regardless of national/non-national status).
Even when it is not a national province, you get some manpower (I read it as the non-national rate of .005, which is one third of what you get from national provinces. Less if the province is overseas.
IC and manpower contribute to your pool, and use your supply chain. Maybe this matters more if they are tiny and can't keep up technologically (their IC goes into making substandard units) or if they control islands and might lose transports (they won't be able to build new ones quickly enough, leading to attrition whenever a unit is stationed on an island. I am thinking of you, Caribbean Federation.
Cons:
If you cannot make this your national province via an event, then you only get to use 20% of their IC, and manpower you gain will be somewhat less than the manpower your puppet would stand to gain (.005 vs .015 X .8 = .012--I think).
This adds the most belligerence of any option.
Mild resource penalty: -10%
Make Them a Puppet!
Pros:
They (not you) get to use 60% of their IC; three times better than the 20% non-national provinces get.
More manpower than non-national provinces (see con section above)
Full harvesting of resources, which can be shipped back to the motherland.
Less belligerence than annexation.
Total control over the government; they will never leave your alliance.
No Partisans; frees up TC (thank you Eugenioso)
Cons:
No control over their build que
Smaller puppets will fall behind a bit in technology
Bonuses not as good as a free country (meaning why don't you liberate it?)
Free the Puppet!
Pros:
They (not you) get to use all of their IC, MP, and resources
If you liberated them, they will (depending on game settings in misc.txt, I think) join your alliance and really like you. They will have the same political slider settings as you.
Lowers your belligerence.
Still no partisan activity.
Cons:
No control over their build que
Smaller nations will fall behind a bit in technology.
Smaller nations with islands can lose convoys, and I don't think you can give them convoys to make up for this, which effectively makes any islands they control into deathcamps for your garisons (starvation).
If your alliance is at peace, they can leave the alliance if they decide they hate you. Like if your belligerence is really high. Or (thank you Slavik3000) if they have a "coup" or "election" event.
Tiny (-0.5% to -1.5%?) Dissent penalty for dictatorships.
In summary: Annex places that will eventually become national provinces, make puppets out of countries if you need their resources, and liberate free everyone else.