All ground covers have advantages and disadvantages.
The most popular ground cover in the United States is turfgrass. However from the tone of your question, I assume that you want a ground cover other than turfgrass. Bugleweed is especially partial to wet, shady sites. Remember that English ivy, lilyturf, or liriope will also do well in full sun. The biggest disadvantage to non-turfgrass ground covers is that many people assume they attract snakes and lizards.