Internally geared hubs can be a great thing for the reasons already covered by others here. To me they are just another choice/variety to enjoy. I will say that it is a different style of riding than a derailleur-geared bike, but is an easy adjustment, at least for me. Good sources for information include Dan Burkhart, the late Sheldon Brown, and Tony Hadland's blog. My experience is limited to the old stuff, and I can say that after giving these hubs a serious try I will never not own one. I don't have a preference one way or another between derailleurs and IGHs. Both systems are wonderful. But a well adjusted Sturmey-Archer AW with an appropriately selected gear range (cogs can be changed) is truly something special. Here's one of mine.
Notice the hills of Northeastern PA in the background. This isn't the bike I choose for climbing, but I have ridden it up and out of my valley. Low gear is about 45 inches.