Nice to see a rum thread with some good suggestions.
Out of the gate Zacapa 23 is one of my favorites. The XO is better, and if you can score a bottle of the 15 (haven't seen it on sale here in the US, only on vacation overseas) it is pretty good as well.
Zaya used to be one of my favorites, however I think they recently change the formula and it is a huge step down. The new bottle I saw even went with a twist cap over a cork, and the rum itself is nowhere near as smooth or enjoyable as it was previously. I still have some of the older version that I'll nurse as long as I can.
Pyrat 1623 is a good premium rum. Its little brother Pyrat XO is not bad as a mixer - I personally don't like it straight up because it tends to have an orange flavor.
A surprisingly good line from right next door in Louisiana is Bayou Rum. Their Silver (white rum) is exceptionally good and makes great cocktails or even cuba libres.
I agree with a statement earlier about Bacardi in general, but they do have one rum known as Reserva Limitada that is pretty good. Its just not as common here in the states. The native Puerto Ricans I know don't typically drink Bacardi - they drink Don Q (Anejo or Grand Anejo), or Barrillito (which comes in the 2 star and 3 star version) and recently has come to our area. I saw a couple of bottles in Specs which let me know I no longer needed to nurse my bottles from PR.
A few outliers: the El Dorado line mentioned is pretty good, but I actually enjoy the 15 yr more than the 21 yr. Appleton from Jamaica is classic, but different versions are much better than others. Mt Gay 1703 from Barbados is pretty good as well.
I've been collecting rum for a while, and could add more if you want, but also a decent site to check out is this one:
https://www.rumratings.com/brandsEDIT: This is what I meant about Zaya. If you find the one on the left, definitely buy it. It the bottle looks like the one on the right, it is terrible imo:
http://imgur.com/K3SzKeU