Lots of good picks in this thread already. Hard for me to name a single favorite, as I like rums of different strength/body at different times, but some of my go to rums are:
Chairman's Reserve, from St. Lucia - awesome neat or with a couple rocks.
Flor de Caña rum. I usually drink 7 year old when I'm out, because that's all I can find. At home, I drink 12 year old. The 7 is a bit rough to drink neat, and the 18 y.o. is too refined. 12 y.o. is perfect.
Pusser's Navy Rum: Sweet, strong (84 proof), tons of flavor. I like this one on the rocks with just a splash of Coke.
Don't knock the white rums. They definitely have their place. For a great Hemingway Daiquiri, I use
Ron Matusalem Platino. It has an almost astringent quality that goes perfectly with the lime juice. For the best mojito, I used to love Tommy Bahama White Sand, but I haven't seen it on shelves in a while. There is a distiller closeby, Drum Circle Distilling, in Sarasota, that makes a great white rum that I now use for mojitos,
Siesta Key White Rum.
I'm not much of a fan of spiced rums, but when I do drink one, it's always mixed, and I really don't have a favorite.
Hope this helps!
Keith