Well, I'll put this in terms of "Light, Dark and Spiced" rums that I use for mixing.
Light - Cruzan Light Rum. I love the sweetness on the palate, and it is very versatile. That and being able to buy a handle for < $20 all make it pretty much my house go-to for making any cocktail with white rum as a component.
Dark - ....Hmmm. I'd have to say as of right now, Grand Reserva Zaya. I originally bought it as a sipper and I find it at best mediocre at that. However it really seems to shine when a cocktail calls for a dark rum in it. Appleton 12 y.o. is also quite excellent to my palate, but I've been more leaning towards it as a sipper as of late. And of course on a budget Cruzan Aged Rum settles in a pinch.
Spiced - Hands down Sailor Jerry's. It is versatile and cheap, as a good spiced rum should be. Whenever I get an opportunity to use a flask somewhere I always fill it with the SJ as you can add it to pretty much every juice/soda based drink and improve it. I have a particular fondness for it in ginger ale though.
I don't find myself using overproof rums very often, and while Mount Gay is very good (I love it mixed 1:2 with some coconut water in the summer) I don't buy/use either of them enough for them to really qualify as "favorites". Never bought Flor de Cana 7 but I might consider it when I run down my Zaya.