Rum is one of those stable distilled spirits that has a very long shelf-life. It means you can store it for over ten years and it will still taste the same provided that it is tightly capped and was not exposed to extreme temperature changes.
If the bottle is unopened, it can stay good for 10 years or more unless it has been exposed to direct sunlight, which can affect the color and flavor. If the bottle is opened, it could become contaminated.
Alcohol itself never really goes bad. As long as it is kept in a cool dry place it should last in definitely. That is unless it has some type of added flavoring that could cause it to spoil. Read the information on the bottle. It it can go bad it will have a printed expiration date.