Art of War is pretty huge. Transferring occupation alone is something that should've been in since EU3, and playing without it now sounds horrible (especially since vassals are now so picky about buying land). AoW gives a few other things related to vassals (using subject CBs, designating marches, war objectives they'll sometimes follow if they're feeling up to it) that are nice as well. I would definitely get it as soon as it goes on sale if you develop any serious interest in EU4. It's a real shame they made transferring occupation a paid feature, it should've been free.
Wealth of Nations has a few useful paid features but isn't necessary. Fabricating trade conflict is somewhat useful in some regions to avoid no CB wars, and moving the trade capital can be nice. Babby westerns also get merchants up the butt from trade companies, but those aren't necessary either.
Res Republica's only real feature I recall is the national focus (+2 MP generation in one category for -1 in the others), which is far from essential but pretty nice. Maybe pick it up when it's dirt cheap.
El Dorito adds some interesting things to play around with (the custom nations) but has no useful features outside of specific regions. You could never buy it and play fine.
Conquest of Paradise is the least useful 'expansion', even less so than El Dorito.
TL;DR
AoW is almost essential to play "seriously", WoN/RR add a couple minor useful features, El Dorito/CoP can be passed over entirely.