Wine Enthusiast magazine doesn't just write about wine — they recently ran a good piece on the best Caribbean rums, including tasting notes and scores. They also suggest a variety of ways in which these rums can be enjoyed, and some of the best places in the islands to stay and to drink. It's definitely worth a read.
Here are some of the rums they recommend. I haven't tried all of them yet, but they get good marks from most people.
Mount Gay Extra Old — Wine Enthusiast score: 93 points. An interesting rum that a lot of people love, although it's a bit too whiskey-like for my tastes.
Appleton Estate 12 Year Aged Rum – One of my favorite rums. A superior product, filled with rich flavor.
Bacardi 8 – Wine Enthusiast score: 91 points
Chairman’s Reserve Spiced Rum – Wine Enthusiast score: 96 points